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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
                               ----------------
                               
                            AMENDMENT NO. 2 TO     
                                 SCHEDULE 13E-3
                        RULE 13E-3 TRANSACTION STATEMENT
           (PURSUANT TO SECTION 13(E) OF THE SECURITIES EXCHANGE ACT
                       OF 1934 AND RULE 13E-3 THEREUNDER)
 
                                UAL CORPORATION
                                (Name of Issuer)

                   UAL CORPORATION AND UNITED AIR LINES, INC.
                       (Name of Persons Filing Statement)
 
                  COMMON STOCK, PAR VALUE $5 PER SHARE, OF UAL
                         (Title of Class of Securities)
 
                                 902549 5 10 4
                    (CUSIP Numbers of Classes of Securities)
 
                            LAWRENCE M. NAGIN, ESQ.
                                UAL CORPORATION
                                 P.O. BOX 66100
                            CHICAGO, ILLINOIS 60666
                                 (708) 952-4000
 
          (Name, Address and Telephone Number of Person Authorized to
   Receive Notices and Communications on Behalf of Persons Filing Statement)
 
                                   Copies to:
                            PETER ALLAN ATKINS, ESQ.
                            THOMAS H. KENNEDY, ESQ.
                             ERIC L. COCHRAN, ESQ.
                      SKADDEN, ARPS, SLATE, MEAGHER & FLOM
                                919 THIRD AVENUE
                            NEW YORK, NEW YORK 10022
 
This statement is filed in connection with (check the appropriate box):

a.  x  The filing of solicitation materials or an information statement subject
   --- to Regulation 14A, Regulation 14C, or Rule 13e-3(c) under the Securities
       Exchange Act of 1934.

b.  x  The filing of a registration statement under the Securities Act of 1933.
   ---
c.     A tender offer.
   ---
d.     None of the above.
   ---

Check the following box if the soliciting materials or information statement
referred to in checking box (a) are preliminary copies.  x
                                                        --- 
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<PAGE>
 
                                  INTRODUCTION
   
  This Amendment No. 2 to Schedule 13E-3 relates to a recapitalization (the
"Recapitalization") of UAL Corporation, a Delaware corporation (the "Company"
or "UAL") pursuant to the Amended and Restated Agreement and Plan of
Recapitalization dated as of March 25, 1994, as amended, (the "Plan of
Recapitalization") among UAL, the Air Line Pilots Association, International
("ALPA") and the International Association of Machinists and Aerospace Workers
(the "IAM"). Under the Plan of Recapitalization, each share of common stock,
par value $5 per share, of the Company (the "Old Shares") that is outstanding
at the Effective Time (as defined in the Plan of Recapitalization) will be
converted into, and become a right to receive, one half (0.5) of a share of new
common stock, par value $0.01 per share, of the Company (the "New Shares") and
one one-thousandth of a share of Series D Redeemable Preferred Stock, without
par value, of the Company (the "Series D Redeemable Preferred Stock").
Concurrently with the solicitation of proxies in connection with the Plan of
Recapitalization, United Air Lines, Inc. ("United") expects to offer up to
$382.5 million principal amount of its Series A Debentures due 2004 (the
"Series A Debentures") (the "United Series A Offering") and up to $382.5
million principal amount of its Series B Debentures due 2014 (the "Series B
Debentures" and, together with the Series A Debentures, the "Debentures") (the
"United Series B Offering" and, together with the United Series A Offering, the
"United Debt Offerings") and the Company expects to offer up to 30,600,000
depositary shares (the "Depositary Preferred Shares") representing interests in
$765.0 million liquidation preference of Series B Preferred Stock of the
Company (the "Public Preferred Stock") (the "UAL Preferred Offering" and,
together with the United Series A Offering and the United Series B Offering,
the "Offerings"). Immediately upon issuance, the Company will redeem each one
one-thousandth of a share of Series D Redeemable Preferred Stock for:     
     
    (i) $25.80 in cash,     
     
    (ii) either (a) $15.55 principal amount of Series A Debentures or (b) if
  the United Series A Offering is consummated, the cash proceeds (without
  deducting any underwriting discount or other costs) from the sale thereof
  by United pursuant to the United Series A Offering,     
     
    (iii) either (a) $15.55 principal amount of Series B Debentures or (b) if
  the United Series B Offering is consummated, the cash proceeds (without
  deducting any underwriting discount or other costs) from the sale thereof
  by United pursuant to the United Series B Offering and     
     
    (iv) either (a) Depositary Preferred Shares representing interests in
  $31.10 liquidation preference of Public Preferred Stock or (b) if the UAL
  Preferred Offering is consummated, the cash proceeds (without deducting any
  underwriting discount or other costs) from the sale thereof by the Company
  pursuant to the UAL Preferred Offering.     
   
In addition, the Plan of Recapitalization provides for (1) certain amendments
to the Company's Certificate of Incorporation and Bylaws that will, among other
things, effectuate the Recapitalization and put into place the revised
corporate governance structure contemplated by the Plan of Recapitalization and
(2) the issuance of new classes of preferred stock that will (a) transfer
approximately 55% (which, under certain circumstances may be increased, up to a
maximum of approximately 63%) of the common equity and voting power of the
Company to employee stock ownership plans to be established for the benefit of
certain groups of employees and (b) effectuate the corporate governance
structure referred to above by permitting different constituent groups to elect
members of the Company's Board of Directors.     
 
  The Plan of Recapitalization further provides for certain amendments to the
existing ALPA collective bargaining agreement and IAM collective bargaining
agreements and the creation of a salaried and management employees cost
reduction program, all of which will become effective at the Effective Time and
are estimated to provide United with $8.2 billion in improved operating
earnings over a twelve year period with a net present value of approximately
$4.9 billion. Furthermore, certain employee benefit plans maintained by the
Company and United will be amended to permit employees to acquire substantial
amounts of the New Shares, Public Preferred Stock and the Debentures.
 
                                       1

<PAGE>
 
   
  The Plan of Recapitalization is incorporated by reference as Exhibit 2.1 to
Amendment No. 3 to the Registration Statement on Form S-4 filed by UAL and
United with the Securities and Exchange Commission (the "Commission") on June
10, 1994 from Exhibit 10.1(A) to UAL's Form 8-K dated June 3, 1994.     
 
  This Schedule 13E-3 is being filed jointly by UAL and United. By filing this
Schedule 13E-3, neither UAL nor United concedes that Rule 13e-3 under the
Securities Exchange Act of 1934 (the "Act of 1934") is applicable to the
Recapitalization or any other transactions contemplated by the Plan of
Recapitalization.
   
  The information set forth in the Registration Statement and Amendment No. 3
to the Registration Statement, filed by UAL and United with the Commission on
June 10, 1994, including the Plan of Recapitalization and other exhibits, is
incorporated in its entirety herein by reference. The following is a summary
cross-reference sheet pursuant to General Instruction F of Schedule 13E-3,
showing the location in the Proxy Statement/Joint Prospectus that is a part of
Amendment No. 3 to the Registration Statement and the Plan of Recapitalization
of information required by Schedule 13E-3. To the extent the requirements of
Schedule 13E-3 are met by the Plan of Recapitalization, no attempt is made in
the following cross-reference sheet to distinguish more limited requirements of
the corresponding Form S-4 items which are also referenced.     
 

<TABLE>
<CAPTION>
  SCHEDULE                                  CAPTION OR LOCATION IN THE PROXY
 13E-3 ITEM                                    STATEMENT/JOINT PROSPECTUS
 ----------                                 --------------------------------
 <C>        <S>
 Item 1:    Issuer and Class of Security Subject to the Transaction.

            (a)                      Cover Page; SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Company and United

            (b)                      Cover Page; SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--Purpose of the Meeting;
                                      INTRODUCTION--Voting Rights and Proxy
                                      Information

            (c)                      SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      Market Prices of the Old Shares; Dividends;
                                      MARKET PRICES OF THE SHARES; DIVIDENDS

            (d)                      SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      Market Prices of the Old Shares; Dividends;
                                      MARKET PRICES OF THE SHARES; DIVIDENDS

            (e)                      Not applicable.

            (f)                      Not applicable.

 Item 2:    Identity and Background. SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      The Company and United
                                      The persons filing this schedule are the
                                      issuer (UAL) and its wholly-owned subsidiary
                                      (United).

            (a)-(d)                  Not applicable.

            (e)-(f)                  None.

            (g)                      Not applicable.
</TABLE>

 
 
                                       2

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<TABLE>
<CAPTION>
  SCHEDULE                              CAPTION OR LOCATION IN THE PROXY
 13E-3 ITEM                                STATEMENT/JOINT PROSPECTUS
 ----------                             --------------------------------
 <C>        <S> 
 Item 3:    Past Contacts, Transactions or Negotiations.

            (a)                      Not applicable.

            (b)                      Not applicable.

 Item 4:    Terms of the
            Transaction.

            (a)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization; THE PLAN OF
                                      RECAPITALIZATION; ELECTION OF
                                      DIRECTORS; DESCRIPTION OF SECURITIES

            (b)                      Not applicable.

 Item 5:    Plans or Proposals of the Issuer or Affiliate

            (a)                      Not applicable.

            (b)                      Not applicable.

            (c)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization; SPECIAL FACTORS--
                                      Management Arrangements; THE PLAN OF
                                      RECAPITALIZATION--Revised Governance
                                      Structure; --Terms and Conditions

            (d)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization; THE PLAN OF
                                      RECAPITALIZATION--Terms and
                                      Conditions; UNAUDITED PRO FORMA
                                      FINANCIAL INFORMATION;
                                      CAPITALIZATION

            (e)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization; SPECIAL FACTORS--
                                      Implementation of the "Airline-
                                      Within-an-Airline" (U2)

            (f)                      Not applicable.

            (g)                      Not applicable.

 Item 6:    Source and Amounts of Funds or Other Consideration.

            (a)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization; THE PLAN OF
                                      RECAPITALIZATION--Terms and
                                      Conditions

            (b)                      FEES AND EXPENSES

            (c)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization; DESCRIPTION OF THE
                                      SECURITIES--The Debentures;--The
                                      ESOP Preferred Stock

            (d)                      Not applicable.
</TABLE>

 
 
                                       3

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<TABLE>
<CAPTION>
  SCHEDULE                                  CAPTION OR LOCATION IN THE PROXY
 13E-3 ITEM                                    STATEMENT/JOINT PROSPECTUS
 ----------                                 --------------------------------
 <C>        <S>
 Item 7:    Purpose(s), Alternatives, Reasons and Effects.

            (a)                      SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      Background of the Recapitalization;
                                      BACKGROUND OF THE PLAN OF RECAPITALIZATION;
                                      SPECIAL FACTORS--Purpose and Structure of
                                      the Recapitalization

            (b)                      BACKGROUND OF THE PLAN OF RECAPITALIZATION

            (c)                      SPECIAL FACTORS--Purpose and Structure of the
                                      Recapitalization
            (d)                      SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      The Plan of Recapitalization; BACKGROUND OF
                                      THE PLAN OF RECAPITALIZATION; SPECIAL
                                      FACTORS--Certain Company Analyses; --Certain
                                      Revenue and Earnings Scenarios; --Effect of
                                      the Recapitalization on Income Statement,
                                      Book Equity and Cash Flow;--Implementation
                                      of the "Airline-Within-an-Airline" (U2); --
                                      Unit Costs; CERTAIN FEDERAL INCOME TAX
                                      CONSEQUENCES

 Item 8:    Fairness of the Transaction.

            (a)                      SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      The Plan of Recapitalization--Recommendation
                                      of the Board; BACKGROUND OF THE PLAN OF
                                      RECAPITALIZATION; SPECIAL FACTORS--
                                      Recommendation of the Board

            (b)                      SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      The Plan of Recapitalization--Recommendation
                                      of the Board; SPECIAL FACTORS--
                                      Recommendation of the Board

            (c)                      SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      Vote Required; INTRODUCTION--Voting Rights
                                      and Proxy Information

            (d)                      SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      The Plan of Recapitalization--Opinions of
                                      Financial Advisors to the Board; SPECIAL
                                      FACTORS--Opinions of the Financial Advisors
                                      to the Board

            (e)                      SUMMARY OF PROXY STATEMENT/JOINT PROSPECTUS--
                                      The Plan of Recapitalization--Recommendation
                                      of the Board; SPECIAL FACTORS--
                                      Recommendation of the Board

            (f)                      Not applicable
</TABLE>

 
 
                                       4

<PAGE>
 

<TABLE>
<CAPTION>
  SCHEDULE                            CAPTION OR LOCATION IN THE PROXY
 13E-3 ITEM                              STATEMENT/JOINT PROSPECTUS
 ----------                           --------------------------------
 <C>        <S> 
 Item 9:    Reports, Opinions, Appraisals and Certain Negotiations.

            (a)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization--Opinions of the
                                      Financial Advisors to the Board;
                                      BACKGROUND OF THE PLAN OF
                                      RECAPITALIZATION; SPECIAL
                                      FACTORS--Opinions of the
                                      Financial Advisors to the Board;
                                      EXPERTS

            (b)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization--Opinions of the
                                      Financial Advisors to the Board;
                                      BACKGROUND OF THE PLAN OF
                                      RECAPITALIZATION; SPECIAL
                                      FACTORS--Opinions of the
                                      Financial Advisors to the Board;
                                      EXPERTS

            (c)                      INCORPORATION OF CERTAIN DOCUMENTS
                                      BY REFERENCE; Opinions of CS
                                      First Boston Corporation and
                                      Lazard Freres & Co. are attached
                                      to the Proxy Statement/Joint
                                      Prospectus as Annexes I and II,
                                      respectively

 Item 10:   Interest in Securities of the Issuer.

            (a)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--Vote Required

            (b)                      Not applicable.

 Item 11:   Contracts, Arrangements or Understandings with Respect to
            the Issuer's Securities.

                                     SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization; THE PLAN OF
                                      RECAPITALIZATION--Terms and
                                      Conditions;--Establishment of
                                      ESOPs;--Revised Governance
                                      Structure; DESCRIPTION OF
                                      SECURITIES

 Item 12:   Present Intention and Recommendation of Certain Persons with
            Regard to the Transaction.

            (a)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--Vote Required;
                                      INTRODUCTION--Voting Rights and
                                      Proxy Information.

            (b)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--Vote Required;
                                      INTRODUCTION--Voting Rights and
                                      Proxy Information.

 Item 13:   Other Provisions of the Transaction.

            (a)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--No Appraisal Rights;
                                      INTRODUCTION

            (b)                      Not applicable.

            (c)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization--Conditions to
                                      the Recapitalization; THE PLAN OF
                                      RECAPITALIZATION--Terms and
                                      Conditions--Conditions
</TABLE>

 
 
                                       5

<PAGE>
 

<TABLE>
<CAPTION>
  SCHEDULE                              CAPTION OR LOCATION IN THE PROXY
 13E-3 ITEM                                STATEMENT/JOINT PROSPECTUS
 ----------                             --------------------------------
 <C>        <S>
 Item 14:   Financial Information.

            (a)                      INCORPORATION OF CERTAIN DOCUMENTS BY
                                      REFERENCE; SUMMARY OF PROXY
                                      STATEMENT/JOINT PROSPECTUS--Selected
                                      Consolidated Historical and Pro
                                      Forma Operating Information;
                                      SELECTED CONSOLIDATED HISTORICAL AND
                                      PRO FORMA FINANCIAL AND OPERATING
                                      INFORMATION

            (b)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--Selected Consolidated
                                      Historical and Pro Forma Operating
                                      Information; UNAUDITED PRO FORMA
                                      FINANCIAL INFORMATION

 Item 15:   Persons or Assets Employed, Retained or Utilized.

            (a)                      COVER PAGE; SUMMARY OF PROXY
                                      STATEMENT/JOINT PROSPECTUS--The Plan
                                      of Recapitalization--Opinions of the
                                      Financial Advisors to the Board;
                                      SPECIAL FACTORS--Opinions of the
                                      Financial Advisors to the Board; THE
                                      PLAN OF RECAPITALIZATION--Terms and
                                      Conditions; FEES AND EXPENSES

            (b)                      SUMMARY OF PROXY STATEMENT/JOINT
                                      PROSPECTUS--The Plan of
                                      Recapitalization; SPECIAL FACTORS--
                                      Opinions of the Financial Advisors
                                      to the Board; --Opinion of Valuation
                                      Firm; INDEPENDENT PUBLIC
                                      ACCOUNTANTS; EXPERTS; LEGAL OPINION;
                                      PROXY SOLICITATION

  Item 16:  Additional Information   None.
</TABLE>

 
 
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<PAGE>
 

<TABLE>
<CAPTION>
  SCHEDULE                              CAPTION OR LOCATION IN THE PROXY
 13E-3 ITEM                                STATEMENT/JOINT PROSPECTUS
 ----------                             --------------------------------
 <C>        <S>
  Item 17:  Material to be Filed as Exhibits
 
 
            (a)(1)                   Indenture dated as of July 1, 1991
                                      between United and The Bank of New
                                      York providing for the issuance of
                                      Senior Debt Securities in series
                                      (filed as Exhibit 4(a) of United's
                                      Registration Statement on Form S-3
                                      (No. 33-57192) and incorporated
                                      herein by reference).

            (a)(2)                   Form of Officer's Certificate relating
                                      to United's Series A Debentures due
                                      2004 and United's Series B Debentures
                                      due 2014 (filed as Schedule 1.3 to
                                      Exhibit 10.1 of UAL's Form
                                      8-K dated March 28, 1994 and
                                      incorporated herein by reference).

            +(b)(1)                  Presentation to the UAL Corporation
                                      Board of Directors by CS First Boston
                                      Corporation and Lazard Freres & Co.
                                      dated December 16, 1993.

            +(b)(2)                  Presentation to the UAL Corporation
                                      Board of Directors by CS First Boston
                                      Corporation and Lazard Freres & Co.
                                      dated December 22, 1993.

            +(b)(3)                  Presentation to the UAL Corporation
                                      Board of Directors by CS First Boston
                                      Corporation and Lazard Freres & Co.
                                      dated March 14, 1994.

            (c)(1)                   Same as item filed as Exhibit (a)(1).

            (c)(2)                   Same as Item filed as Exhibit (a)(2).

            (c)(3)                   Proposed Restated Certificate of
                                      Incorporation of UAL Corporation
                                      (filed as Exhibit 10.1(B) of UAL's
                                      Form 8-K dated June 3, 1994 and
                                      incorporated herein by reference).

            (d)(1)                   Chairman's Letter to Stockholders,
                                      Notice of Meeting of Stockholders and
                                      the Proxy Statement/Joint Prospectus
                                      (filed as a part of UAL's and
                                      United's Amendment No. 3 to the
                                      Registration Statement on Form S-4
                                      dated June 10, 1994 and incorporated
                                      herein by reference).

            (e)                      Not applicable.

            (f)                      Not applicable.
</TABLE>

 
+Previously filed.
 
                                       7

<PAGE>
 
                                   SIGNATURE
 
  After due inquiry, and to the best of my knowledge and belief, the
undersigned certifies that the information set forth in this statement is true,
complete and correct.
 
                                          UAL Corporation
 
                                                     /s/ John C. Pope
                                          By: _________________________________
                                                       John C. Pope
                                               Director, President and 
                                               Chief Operating Officer
   
Date: June 15, 1994     
 
                                       8

<PAGE>
 
                                   SIGNATURE
 
  After due inquiry, and to the best of my knowledge and belief, the
undersigned certifies that the information set forth in this statement is true,
complete and correct.
 
                                          United Air Lines, Inc.
 
                                                     /s/ John C. Pope
                                          By: _________________________________
                                                        John C. Pope 
                                                   Director, Chairman and 
                                                   Chief Executive Officer
   
Date: June 15, 1994     
 
                                       9