<PAGE>

                                                                    EXHIBIT 10.6

               SUPPLEMENT NO. 2 TO AMENDED AND RESTATED INDENTURE

          This SUPPLEMENT NO. 2 TO AMENDED AND RESTATED INDENTURE, dated as of
October 15, 2002 (this "Supplement"), is entered into among AMERICREDIT MASTER
TRUST, a Delaware business trust (the "Issuer"), BANK ONE, NA, a national
banking association, as trustee (the "Trustee") and as trust collateral agent
(the "Trust Collateral Agent"), and DEUTSCHE BANK TRUST COMPANY AMERICAS
(formerly known as Bankers Trust Company), as administrative agent (the
"Administrative Agent").

                                    RECITALS

          1.   The Issuer, Trustee, Trust Collateral Agent, and the
Administrative Agent are parties to that certain Amended and Restated Indenture
dated as of February 22, 2002 (as previously amended and as amended,
supplemented or otherwise modified from time to time, the "Indenture").

          2.   Pursuant to Section 9.1 of the Indenture, the parties hereto
desire to amend and supplement the Indenture without the consent of the Holders
of the Notes to increase the Class A Credit Score Enhancement Rate, the Class B
Credit Score Enhancement Rate and/or the Class C Credit Score Enhancement Rate.

          NOW, THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties agree as follows:

          1.   Certain Defined Terms. Capitalized terms that are used herein
without definition and that are defined in the Indenture shall have the same
meanings herein as therein.

          2.   Amendments to Indenture. The Indenture is hereby amended by
deleting Schedule 2 thereto in its entirety and substituting, in lieu thereof,
Schedule 2 to this Supplement.

          3.   Effect of Supplement. Except as expressly amended and modified by
this Supplement, all provisions of the Indenture shall remain in full force and
effect. After this Supplement becomes effective, all references in the Indenture
and the Related Documents to "this Indenture" or words of similar effect
referring to the Indenture shall be deemed to be references to the Indenture as
amended by this Supplement. This Supplement shall not be deemed to expressly or
impliedly waive, amend or supplement any provision of the Indenture other than
as expressly set forth herein.

          4.   Effectiveness. This Supplement shall become effective as of the
date hereof upon receipt by the Trustee of counterparts of this Supplement
(whether by facsimile or otherwise) executed by each of the other parties hereto
and receipt by the Trustee of an opinion of counsel satisfying the requirements
of Section 9.3 of the Indenture.

          5.   Counterparts. This Supplement may be executed in any number of
counterparts and by different parties on separate counterparts, and each
counterpart shall be deemed to be an original, and all such counterparts shall
together constitute but one and the same instrument.

<PAGE>

          6.   Governing Law. This Supplement shall be governed by, and
construed in accordance with, the internal laws of the State of New York without
regard to any otherwise applicable principles of conflicts of law.

          7.   Section Headings. The various headings of this Supplement are
inserted for convenience only and shall not affect the meaning or interpretation
of this Supplement, the Indenture or any provision hereof or thereof.

          8.   Representations and Warranties. The Issuer represents and warrant
that (i) all of its representations and warranties set forth in the Indenture
are true and accurate in all material respects as though made on and as of the
date hereof (except representations and warranties which relate to a specific
date, which were true and correct as of such date) and (ii) no Event of Default
under the Indenture has occurred and is continuing.


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<PAGE>

          IN WITNESS WHEREOF, the parties have executed this Supplement as of
the date first written above.

                                       AMERICREDIT MASTER TRUST, as Issuer

                                       By: DEUTSCHE BANK TRUST COMPANY DELAWARE,
                                       not in its individual capacity but solely
                                       as Owner Trustee on behalf of the Trust

                                       By:
                                             -----------------------------------
                                       Name:
                                             -----------------------------------
                                       Title:
                                             -----------------------------------

                                       BANK ONE, N.A., as Trust Collateral
                                       Agent and Trustee

                                       By:
                                             -----------------------------------
                                       Name:
                                             -----------------------------------
                                       Title:
                                             -----------------------------------

                                       DEUTSCHE BANK TRUST COMPANY
                                       AMERICAS (formerly known as Bankers Trust
                                       Company), as Administrative Agent

                                       By:
                                             -----------------------------------
                                       Name:
                                             -----------------------------------
                                       Title:
                                             -----------------------------------

                                       By:
                                             -----------------------------------
                                       Name:
                                             -----------------------------------
                                       Title:
                                             -----------------------------------

<PAGE>


          SCHEDULE 2

          UPDATED: EFFECTIVE OCTOBER 15, 2002

          "Class A Credit Score Enhancement Rate" means, as of any date, the sum
of (1) the Step-Up Percentage and (2) the greater of (a) 17.50% and (b) the
percentage set forth in the following table opposite the Net Spread as of such
date in the column in which the weighted average AmeriCredit Score for the
Eligible Receivables as of such date appears:

CLASS A

<TABLE>
<CAPTION>
                                         Weighted Average AmeriCredit Score
                     220-224           225 to 229        230-234           235-239           240+
Net Spread
<S>                  <C>               <C>               <C>               <C>               <C>
* 9.0%               34.00%            32.10%            33.00%            28.75%            18.50%
* 8.5% and ** 9.0%   34.20%            34.75%            36.00%            31.25%            21.50%
* 8.0% and ** 8.5%   35.00%            36.25%            36.90%            31.25%            24.75%
* 7.5% and ** 8.0%   37.60%            38.00%            37.75%            35.00%            25.00%
* 7.0% and ** 7.5%   37.20%            37.25%            38.50%            37.25%            26.25%
* 6.5% and ** 7.0%   41.70%            38.75%            38.50%            40.75%            29.50%
* 6.0% and ** 6.5%   42.40%            42.00%            41.00%            43.00%            34.00%
* 5.5% and ** 6.0%   48.10%            43.75%            40.00%            43.00%            34.00%
</TABLE>

* means greater than
** means less than or equal to

          "Class B Credit Score Enhancement Rate" means, as of any date, the sum
of (1) the Step-Up Percentage and (2) the greater of (a) 12.00% and (b) the
percentage set forth in the following table opposite the Net Spread as of such
date in the column in which the weighted average AmeriCredit Score for the
Eligible Receivables as of such date appears:

CLASS B

<TABLE>
<CAPTION>
                                         Weighted Average AmeriCredit Score
                     220-224           225 to 229        230-234           235-239           240+
Net Spread
<S>                  <C>               <C>               <C>               <C>               <C>
* 9.0%               26.60%            29.25%            29.50%            25.75%            15.00%
* 8.5% and ** 9.0%   26.90%            30.75%            32.00%            28.25%            17.50%
* 8.0% and ** 8.5%   27.70%            32.25%             32.9%            28.25%            20.75%
</TABLE>

* means greater than
** means less than or equal to

<PAGE>

<TABLE>
<S>                  <C>               <C>               <C>               <C>               <C>
* 7.5% and ** 8.0%   28.40%            33.25%            34.20%            31.25%            21.50%
* 7.0% and ** 7.5%   30.20%            33.25%            34.50%            33.25%            23.25%
* 6.5% and ** 7.0%   31.70%            34.00%            34.50%            36.75%            25.50%
* 6.0% and ** 6.5%   33.40%            35.75%            35.50%            39.00%            29.00%
* 5.5% and ** 6.0%   35.10%            36.50%            35.50%            39.00%            29.00%
</TABLE>

* means greater than
** means less than or equal to

          "Class C Credit Score Enhancement Rate" means, as of any date, the sum
of (1) the Step-Up Percentage and (2) the greater of (a) 5.50% and (b) the
percentage set forth in the following table opposite the Net Spread as of such
date in the column in which the weighted average AmeriCredit Score for the
Eligible Receivables as of such date appears:

CLASS C

<TABLE>
<CAPTION>

                               Weighted Average AmeriCredit Score
                     220-224           225 to 229        230-234           235-239           240+
Net Spread
<S>                  <C>               <C>               <C>               <C>               <C>
* 9.0%               18.00%            15.25%            12.50%             9.75%             8.50%
* 8.5% and ** 9.0%   20.50%            15.75%            13.00%            10.25%             8.50%
* 8.0% and ** 8.5%   20.60%            16.25%            13.90%            11.25%             8.50%
* 7.5% and ** 8.0%   20.50%            17.25%            14.70%            11.75%             9.50%
* 7.0% and ** 7.5%   21.00%            18.25%            15.50%            12.25%            10.00%
* 6.5% and ** 7.0%   21.50%            19.00%            16.50%            12.75%            10.50%
* 6.0% and ** 6.5%   22.00%            19.75%            17.50%            13.25%            11.00%
* 5.5% and ** 6.0%   22.50%            20.50%            18.50%            14.25%            12.00%
</TABLE>

* means greater than
** means less than or equal to

          "Class D Credit Score Enhancement Rate" shall have the meaning, if
any, set forth in a supplement or amendment to the Indenture.

          "Class E Credit Score Enhancement Rate" shall have the meaning, if
any, set forth in a supplement or amendment to the Indenture.

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