<PAGE>   1
                                 EXHIBIT 4.2                   CONFORMED COPY

                    AMENDMENT dated as of January 26, 2001 (this "Amendment"),
               to the 364-Day Revolving Credit Agreement (the "364-Day Credit
               Agreement") dated as of August 15, 2000, among THE GOODYEAR TIRE
               & RUBBER COMPANY, an Ohio corporation (the "Borrower"); the
               lenders party thereto (the "Lenders"); and THE CHASE MANHATTAN
               BANK, a New York banking corporation, as administrative agent for
               the Lenders (in such capacity, the "Agent").

               The Borrower has requested that the Lenders amend certain
provisions of the 364-Day Credit Agreement, and the Lenders are willing so to
amend the 364-Day Credit Agreement, on the terms and subject to the conditions
set forth herein. Capitalized terms used herein and not otherwise defined herein
shall have the meanings assigned to such terms in the 364-Day Credit Agreement.

               Accordingly, in consideration of the mutual agreements herein
contained and other good and valuable consideration, the sufficiency and receipt
of which are hereby acknowledged, the parties hereto agree as follows:

               SECTION 1. Amendment of 364-Day Credit Agreement. The 364-Day
Credit Agreement is hereby amended, effective as of the Amendment Effective
Date, as follows:

               (a) Amendment of Section 1.01. Section 1.01 of the 364-Day Credit
Agreement is hereby amended as follows:

                    (i) The following definitions are hereby inserted in
          alphabetical order in Section 1.01 of the 364-Day Credit Agreement:

                    ""Applicable Spread" shall mean, as at the date as of which
          any determination in respect thereof is being or to be made, the
          applicable percentage set forth below under the caption "Eurodollar
          Spread" or "CD Spread", as the case may be, based upon the Leverage
          Ratio as of the last day of the relevant fiscal quarter:
<TABLE>
<CAPTION>

CATEGORY             LEVERAGE RATIO                      EURODOLLAR SPREAD                CD SPREAD
--------             --------------                      -----------------                ---------
<S>                  <C>                                      <C>                          <C>
1                    less than or equal to 25%                 0.4000%                      0.5250%

2                    greater than 25% but less than            0.5000%                      0.6250%
                     or equal to 40%

3                    greater than 40% but less than            0.8500%                      0.9750%
                     or equal to 55%

4                    greater than 55%                          1.0500%                      1.1750%

</TABLE>
          Each change in the Applicable Spread resulting from a change in the
          Leverage Ratio as of the end of any fiscal quarter will be effective
          as of the date of delivery by the Borrower of a certificate setting
          forth the calculation of the Leverage Ratio as at the end of such
          fiscal quarter, which certificate shall be delivered with the annual
          and/or


                                    X-4.2-1



<PAGE>   2
                                                                              2

          quarterly financial statements for such fiscal quarter required to be
          delivered under paragraph (c) of Article V. Notwithstanding the
          foregoing, at any time that the Borrower shall fail to deliver to the
          Agent such certificate by the time required under such paragraph (c),
          the Applicable Spread shall be deemed to be that corresponding to
          Category 4 until such time as the Borrower shall so deliver such
          certificate."

               ""Facility Fee Percentage" shall mean, as at the date as of which
          any determination in respect thereof is being or to be made, the
          applicable percentage set forth below based upon the Leverage Ratio as
          of the last day of the relevant fiscal quarter:

<TABLE>
<CAPTION>
CATEGORY                  LEVERAGE RATIO                         FACILITY FEE PERCENTAGE
--------                  --------------                         -----------------------
<S>                       <C>                                            <C>
1                         less than or equal to 25%                       0.1000%

2                         greater than 25% but less than                  0.1250%
                          or equal to 40%

3                         greater than 40% but less than                  0.1500%
                          or equal to 55%

4                         greater than 55%                                0.2000%
</TABLE>

          The Leverage Ratio shall be determined at the end of each fiscal
          quarter of Borrower and shall be effective in respect of the entire
          next succeeding fiscal quarter of Borrower. The Borrower shall deliver
          a certificate setting forth the calculation of the Leverage Ratio with
          respect to the end of each fiscal quarter, which certificate shall be
          delivered with the annual and quarterly financial statements required
          to be delivered under paragraph (c) of Article V. Notwithstanding the
          foregoing, at any time that the Borrower shall fail to deliver to the
          Agent such certificate by the time required under such paragraph (c),
          the Facility Fee Percentage shall be deemed to be that corresponding
          to Category 4 until such time as the Borrower shall so deliver such
          certificate."

               ""Leverage Ratio" shall mean, as at the end of any fiscal quarter
          in respect of which a determination thereof is being or to be made,
          the quotient (expressed as a percentage) of (a) the sum of (i) "notes
          payable to banks and overdrafts", plus (ii) "long term debt due within
          one year", plus (iii) "long term debt and capital leases" (as each
          such item is reported on the Consolidated balance sheet of the
          Borrower and the Subsidiaries as at the end of such fiscal quarter),
          plus (iv) the net proceeds from the sale of domestic accounts
          receivable outstanding at the end of such fiscal quarter (determined
          in a manner consistent with that used in preparing the Borrower's 1999
          Annual Report on Form 10-K), divided by (b) the sum of (i)
          Consolidated Net Worth (without giving effect to the exclusion
          contained in clause (ii) of the definition of the term "Consolidated
          Net Worth" and without giving effect to the $499.3 million after-tax
          writedown of the Borrower's Oil Transportation Segment Assets in
          December of 1996, plus (ii) the sum obtained pursuant to clause (a)
          above."


                                    X-4.2-2

<PAGE>   3
                                                                              3

               ""Net Income" shall mean, with respect to any Annual Period in
          respect of which a determination is being made or to be made,
          consolidated net income of the Borrower and the Subsidiaries for such
          period determined in accordance with generally accepted accounting
          principles in the United States, as in effect on the Closing Date."

               (ii) The definition of "Consolidated Operating Income" is hereby
          amended by inserting the phrase ", depreciation and amortization"
          immediately following the word "income" in such definition.

          (b) Amendment of Section 2.06. Section 2.06 of the 364-Day Credit
Agreement is hereby amended as follows:

               (i) Paragraph (a) of Section 2.06(a) is hereby amended by
          replacing the phrase "0.10% per annum" with the phrase "the applicable
          Facility Fee Percentage per annum".

               (ii) Paragraph (b) of Section 2.06 is hereby amended by deleting
          the reference to ".125%" with "0.250%".

          (c) Amendment of Section 2.08. Section 2.08 of the 364-Day Credit
Agreement is hereby amended as follows:

               (i) Paragraph (a) of Section 2.08 is hereby amended by deleting
          the reference to "0.40%" in clause (i) thereof and replacing it with
          the phrase "the Eurodollar Spread".

               (ii) Paragraph (b) of Section 2.08 is hereby amended by deleting
          the reference to "0.525%" and replacing it with the phrase "the CD
          Spread".

               (iii) Paragraph (c) of Section 2.08 is hereby amended by deleting
          the reference to "0.10%" and replacing it with the phrase "the
          Facility Fee Percentage in effect from time to time during the
          Interest Period applicable to such ABR Borrowing".

          (d) Amendment of Article V. Article V of the 364-Day Credit Agreement
is hereby amended as follows:

               (i) Paragraph (a) of Article V is hereby deleted in its entirety
          and replaced with the following paragraph:

                    "(a) Interest Coverage Ratio". Maintain, as at the end of
               each fiscal quarter of the Borrower, a ratio of Consolidated
               Operating Income for the Annual Period then ended to Consolidated
               Interest Expense for such Annual Period of not less than the
               ratio set forth below opposite such period:






                                     X-4.2-3

<PAGE>   4
                                                                              4

<TABLE>
<CAPTION>
               PERIOD ENDING                                   MINIMUM RATIO
               -------------                                   -------------
<S>                                                             <C>
               March 31, 2001                                  2.60 to 1.00
               June 30, 2001                                   2.60 to 1.00
               September 30, 2001                              2.75 to 1.00
               December 31, 2001 and each
               Annual Period ending thereafter                 3.50 to 1.00
</TABLE>

               (ii) Paragraph (b) of Article V is hereby amended by replacing
          the reference to "$1,250,000,000" with the phrase "$2,800,000,000 plus
          50% of the cumulative amount of Net Income for each fiscal quarter
          ended after December 31, 2000 and excluding any such fiscal quarter
          for which Net Income shall have been negative."

          (e) Amendment of Article VI. Article VI of the 364-Day Credit
Agreement is hereby amended by inserting the following new paragraph at the end
thereof:

                     "(e) Negative Pledge. Enter into, or permit any Subsidiary
               organized under the laws of the United States or any state,
               territory or possession thereof to enter into, any covenant or
               other agreement that by its terms limits the ability of the
               Borrower or any such Subsidiary to pledge its accounts receivable
               or inventory or proceeds thereof to secure indebtedness."

          SECTION 2. Representations and Warranties. To induce the other parties
hereto to enter into this Amendment, the Borrower represents and warrants to
each of the Lenders and the Agent that, as of the Amendment Effective Date:

          (a) This Amendment has been duly authorized, executed and delivered by
the Borrower and constitutes the legal, valid and binding obligation of the
Borrower enforceable against the Borrower in accordance with its terms subject
to applicable bankruptcy, insolvency, reorganization, moratorium or other
similar laws affecting creditors' rights generally and subject, as to
enforceability, to general principles of equity (regardless of whether such
enforceability is considered in a proceeding at law or in equity).

          (b) The representations and warranties set forth in Article III of the
364-Day Credit Agreement are true and correct in all material respects on and as
of the Amendment Effective Date with the same effect as though made on and as of
the Amendment Effective Date, except to the extent such representations and
warranties expressly relate to an earlier date.

          (c) No Event of Default has occurred and is continuing.

          The foregoing representations shall be deemed to have been made
pursuant to and in accordance with Section 4.01 of the Credit Agreement.



                                     X-4.2-4


<PAGE>   5
                                                                              5

          SECTION 3. Amendment Fee. In consideration of the agreements of the
Lenders contained in Section 1 of this Amendment, the Borrower agrees to pay to
the Agent, for the account of each Lender that delivers an executed counterpart
of this Amendment prior to 12:00 noon (New York City time), on Friday, January
26, 2001, an amendment fee (an "Amendment Fee") in an amount equal to 0.15% of
the amount of such Lender's Commitment, whether used or unused.

          SECTION 4. Effectiveness. This Amendment shall become effective on the
date (the "Amendment Effective Date") that the Agent shall have received (a)
counterparts of this Amendment that, when taken together, bear the signatures of
the Borrower and the Majority Lenders and (b) the Agent shall have received the
Amendment Fee.

          SECTION 5. Effect of Amendment. Except as expressly set forth herein,
this Amendment shall not by implication or otherwise limit, impair, constitute a
waiver of or otherwise affect the rights and remedies of the Lenders or the
Agent under the 364-Day Credit Agreement or any other document related thereto,
and shall not alter, modify, amend or in any way affect any of the terms,
conditions, obligations, covenants or agreements contained in the 364-Day Credit
Agreement or any other provision of the 364-Day Credit Agreement or any other
document related thereto, all of which are ratified and affirmed in all respects
and shall continue in full force and effect. This Amendment shall apply and be
effective only with respect to the provisions of the 364-Day Credit Agreement
specifically referred to herein.

          SECTION 6. Counterparts. This Amendment may be executed in any number
of counterparts and by different parties hereto in separate counterparts, each
of which when so executed and delivered shall be deemed an original, but all
such counterparts together shall constitute but one and the same instrument.
Delivery of any executed counterpart of a signature page of this Amendment by
facsimile transmission shall be as effective as delivery of a manually executed
counterpart hereof.

          SECTION 7. Applicable Law. THIS AMENDMENT SHALL BE GOVERNED BY, AND
CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

          SECTION 8. Headings. The headings of this Amendment are for purposes
of reference only and shall not limit or otherwise affect the meaning hereof.




                                     X-4.2-5


<PAGE>   6
                                                                              6

          IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be duly executed by their duly authorized officers, all as of the date and year
first above written.

                                  THE GOODYEAR TIRE & RUBBER COMPANY

                                  by
                                      /s/ Stephanie Bergeron
                                      -----------------------------------------
                                      Name: Stephanie Bergeron
                                      Title: Vice President & Treasurer

                                  THE CHASE MANHATTAN BANK,
                                  individually and as Agent

                                  by
                                      /s/ Julie S. Long
                                      -----------------------------------------
                                      Name: Julie S. Long
                                      Title: Vice President

                                  ABN AMRO BANK N.V.,

                                  by
                                      /s/ John M. Ellenwood
                                      -----------------------------------------
                                      Name: John M. Ellenwood
                                      Title: Group Vice President

                                  by
                                      /s/ John J. Mack
                                      -----------------------------------------
                                      Name: John J. Mack
                                      Title: Group Vice President

                                  BANCA NAZIONALE DEL LAVORO S.p.A,
                                  NEW YORK BRANCH,

                                  by
                                      /s/ Giulio Giovine
                                      -----------------------------------------
                                      Name: Giulio Giovine
                                      Title: Vice President

                                  by
                                      /s/ Leonardo Valentini
                                      -----------------------------------------
                                      Name: Leonardo Valentini
                                      Title: First Vice President











                                     X-4.2-6

<PAGE>   7
                                                                              7

                                  THE BANK OF NOVA SCOTIA,

                                  by
                                      /s/ A.S. Norsworthy
                                      -----------------------------------------
                                      Name: A.S. Norsworthy
                                      Title: Senior Team Leader-Loan Operations

                                  BANK OF TOKYO-MITSUBISHI TRUST COMPANY,

                                  by
                                      /s/ Friedrich N. Wilms
                                      -----------------------------------------
                                      Name: Friedrich N. Wilms
                                      Title: VP & Global Relationship Manager

                                  BANK ONE, N.A.,

                                  by
                                      /s/ Kelly M Hamrick
                                      -----------------------------------------
                                      Name: Kelly M. Hamrick
                                      Title: Vice President

                                  BARCLAYS BANK PLC,

                                  by
                                      /s/ L. Peter Yetman
                                      -----------------------------------------
                                      Name: L. Peter Yetman
                                      Title: Director

                                  BBL INTERNATIONAL (U.K.) LIMITED,

                                  by
                                      /s/ C.F. Wright
                                      -----------------------------------------
                                      Name: C.F. Wright
                                      Title: Authorised Signatory

                                  by
                                      /s/ M-C Swinnen
                                      -----------------------------------------
                                      Name: M-C Swinnen
                                      Title: Authorised Signatory











                                     X-4.2-7

<PAGE>   8
                                                                              8
                                  BNP PARIBAS,

                                  by
                                      /s/ Frederick H. Moryl, Jr.
                                      -----------------------------------------
                                      Name: Frederick H. Moryl, Jr.
                                      Title: Director

                                  by
                                      /s/ Richard L. Sted
                                      -----------------------------------------
                                      Name: Richard L. Sted
                                      Title: Managing Director-
                                             Central Region Mgr.

                                  CIBC INC.,

                                  by
                                      /s/ Dominic J. Sorresso
                                      -----------------------------------------
                                      Name: Dominic J. Sorresso
                                      Title: Executive Director
                                             CIBC World Markets Corp., as Agent

                                  CITICORP USA, INC.,

                                  by
                                      /s/ Brian Ike
                                      -----------------------------------------
                                      Name: Brian Ike
                                      Title: Vice President

                                  COMMERZBANK AKTIENGESELLSCHAFT,
                                  NEW YORK AND GRAND CAYMAN BRANCHES,

                                  by
                                      /s/ Graham A Warning
                                      -----------------------------------------
                                      Name: Graham A Warning
                                      Title: Assistant Treasurer

                                  by
                                      /s/ John Marlatt
                                      -----------------------------------------
                                      Name: John Marlatt
                                      Title: Vice President




                                     X-4.2-8


<PAGE>   9
                                                                              9
                                  CREDIT LYONNAIS, CHICAGO BRANCH,

                                  by
                                      /s/ Nigel R. Carter
                                      -----------------------------------------
                                      Name: Nigel R. Carter
                                      Title: Vice President

                                  CREDIT SUISSE FIRST BOSTON,

                                  by
                                      /s/ Kristin Lepri
                                      -----------------------------------------
                                      Name: Kristin Lepri
                                      Title: Associate

                                  by
                                      /s/ David L. Sawyer
                                      -----------------------------------------
                                      Name: David L. Sawyer
                                      Title: Vice President

                                  THE DAI-ICHI KANGYO BANK, LTD.,

                                  by
                                      /s/ Nobuyasu Fukatsu
                                      -----------------------------------------
                                      Name: Nobuyasu Fukatsu
                                      Title: General Manager

                                  DEUTSCHE BANK AG NEW YORK BRANCH
                                  AND/OR CAYMAN ISLANDS BRANCH,

                                  by
                                      /s/ Hans-Josef Thiele
                                      -----------------------------------------
                                      Name: Hans-Josef Thiele
                                      Title: Director

                                  by
                                      /s/ Oliver Schwarz
                                      -----------------------------------------
                                      Name: Oliver Schwarz
                                      Title: Vice President





                                     X-4.2-9
<PAGE>   10


                                                                             10

                                  DRESDNER BANK AG NEW YORK AND CAYMAN
                                  BRANCHES,

                                  by
                                      /s/ Faraaz Kamran
                                      -----------------------------------------
                                      Name: Faraaz Kamran
                                      Title: Assistant Vice President

                                  by
                                      /s/ Thomas Hasenauer
                                      -----------------------------------------
                                      Name: Thomas Hasenauer
                                      Title: Assistant Treasurer

                                  THE INDUSTRIAL BANK OF JAPAN, LIMITED,

                                  by
                                      /s/ Walter R. Wolff
                                      -----------------------------------------
                                      Name: Walter R. Wolff
                                      Title: Joint General Manager

                                  KEYBANK NATIONAL ASSOCIATION,

                                  by
                                      /s/ Daniel W. Lally
                                      -----------------------------------------
                                      Name: Daniel W. Lally
                                      Title: Assistant Vice President

                                  NATIONAL CITY BANK,

                                  by
                                      /s/ Janice E. Focke
                                      -----------------------------------------
                                      Name: Janice E. Focke
                                      Title: Senior Vice President

                                  THE NORTHERN TRUST COMPANY,

                                  by
                                      /s/ Craig L. Smith
                                      -----------------------------------------
                                      Name: Craig L. Smith
                                      Title: Vice President








                                    X-4.2-10
<PAGE>   11


                                                                             11

                                  ROYAL BANK OF CANADA,

                                  by
                                      /s/ Gordon C. MacArthur
                                      -----------------------------------------
                                      Name: Gordon C. MacArthur
                                      Title: Senior Manager

                                  THE SANWA BANK, LIMITED,

                                  by
                                      /s/ Kenneth C. Eichwald
                                      -----------------------------------------
                                      Name: Kenneth C. Eichwald
                                      Title: Senior Vice President

                                  SOCIETE GENERALE,

                                  by
                                      /s/ Anne-Marie Dumortier
                                      -----------------------------------------
                                      Name: Anne-Marie Dumortier
                                      Title: Vice President

                                  STANDARD CHARTERED BANK,

                                  by
                                      /s/ David B. Edwards
                                      -----------------------------------------
                                      Name: David B. Edwards
                                      Title: Senior Vice President

                                  by
                                      /s/ Andrew Y. Ng
                                      -----------------------------------------
                                      Name: Andrew Y. Ng
                                      Title: Vice President

                                  THE SUMITOMO BANK, LIMITED,

                                  by
                                      /s/ Edward D. Henderson, Jr.
                                      -----------------------------------------
                                      Name: Edward D. Henderson, Jr.
                                      Title: Senior Vice President





                                    X-4.2-11