FIRST AMENDMENT TO THE AMENDED AND RESTATED SERIES 2005-2

Exhibit 10.33(b)

CONFORMED COPY

FIRST AMENDMENT TO THE AMENDED AND RESTATED SERIES 2005-2

SUPPLEMENT

This FIRST AMENDMENT (this “Amendment”), dated as of November 11, 2008, amends the Amended and Restated Series 2005-2 Supplement (the “Series 2005-2 Supplement”), dated as of May 20, 2008, and is between AVIS BUDGET RENTAL CAR FUNDING (AESOP) LLC (formerly known as Cendant Rental Car Funding (AESOP) LLC), a special purpose limited liability company established under the laws of Delaware (“ABRCF”) and THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A. (as successor in interest to The Bank of New York Trust Company, N.A.), a national banking association, as trustee (in such capacity, the “Trustee”) and as agent for the benefit of the Series 2005-2 Noteholders and the Surety Provider (in such capacity, the “Series 2005-2 Agent”), to the Second Amended and Restated Base Indenture, dated as of June 3, 2004, between ABRCF and the Trustee (as amended, modified or supplemented from time to time, exclusive of Supplements creating a new Series of Notes, the “Base Indenture”). All capitalized terms used herein and not otherwise defined herein shall have the respective meanings provided therefor in the Definitions List attached as Schedule I to the Base Indenture (as amended through the date hereof) or the Series 2005-2 Supplement, as applicable.

W I T N E S S E T H:

WHEREAS, pursuant to Section 12.2(i) of the Base Indenture, an amendment to any Supplement requires the consent of ABRCF, the Trustee, the applicable Enhancement Provider and each affected Noteholder of the applicable Series of Notes;

WHEREAS, pursuant to Section 6.11 of the Series 2005-2 Supplement, the Surety Provider is deemed to be the sole holder of the Series 2005-2 Notes for the purpose of giving all consents, waivers and approvals under the Series 2005-2 Supplement and the Base Indenture on behalf of the Series 2005-2 Notes;

WHEREAS, ABRCF has requested the Trustee, the Series 2005-2 Agent and the Surety Provider to, and, upon the effectiveness of (i) this Amendment and (ii) the letter (the “Consent Letter”), dated as of the date hereof, among ABRCF and the Surety Provider, ABRCF, the Trustee, the Series 2005-2 Agent and the Surety Provider have agreed to, amend certain provisions of the Series 2005-2 Supplement as set forth herein;

WHEREAS, the parties desire to amend the Series 2005-2 Supplement (1) to increase the Series 2005-2 Maximum Non-Program Vehicle Percentage, (2) to increase the number of Kia, Suzuki and Hyundai vehicles ABRCF can purchase for inclusion in the AESOP I Operating Lease Loan Agreement Borrowing Base (the “Borrowing Base”) and (3) to require a certain percentage of Kia and Hyundai Vehicles to be included at the Series 2005-2 Standard & Poor’s Highest Enhanced Vehicle Percentage in the Borrowing Base; and

WHEREAS, ABRCF has requested the Trustee, the Series 2005-2 Agent and each Noteholder to, and, upon this Amendment becoming effective, ABRCF, the Trustee, the Series 2005-2 Agent and the Surety Provider voting as the deemed sole Noteholder have agreed to, amend certain provisions of the Series 2005-2 Supplement as set forth herein;

NOW, THEREFORE, it is agreed:

1. Each of the following defined terms, as set forth in Article I(b) of the Series 2005-2 Supplement, is hereby amended and restated in its entirety as follows:

“Series 2005-2 Maximum Manufacturer Amount” means, as of any day, any of the Series 2005-2 Maximum Mitsubishi Amount, the Series 2005-2 Maximum Individual Isuzu/Subaru Amount, the Series 2005-2 Maximum Hyundai Amount, the Series 2005-2 Maximum Kia Amount or the Series 2005-2 Maximum Suzuki Amount.

“Series 2005-2 Maximum Non-Program Vehicle Percentage” means, as of any date of determination, the sum of (a) 85% and (b) a fraction, expressed as a percentage, the numerator of which is the aggregate Net Book Value of all Redesignated Vehicles manufactured by a Bankrupt Manufacturer or a Manufacturer with respect to which a Manufacturer Event of Default has occurred, and in each case leased under the AESOP I Operating Lease or the Finance Lease as of such date, and the denominator of which is the aggregate Net Book Value of all Vehicles leased under the Leases as of such date.

“Series 2005-2 Required Enhancement Amount” means, as of any date of determination, the sum of (i) the product of the Series 2005-2 Required Enhancement Percentage as of such date and the Series 2005-2 Invested Amount as of such date, (ii) the Series 2005-2 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the Non-Program Vehicle Amount as of such date over the Series 2005-2 Maximum Non-Program Vehicle Amount as of such date, (iii) the Series 2005-2 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the aggregate Net Book Value of all Vehicles manufactured by Mitsubishi and leased under the Leases as of such date over the Series 2005-2 Maximum Mitsubishi Amount as of such date, (iv) the Series 2005-2 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the aggregate Net Book Value of all Vehicles manufactured by Isuzu or Subaru, individually, and leased under the Leases as of such date over the Series 2005-2 Maximum Individual Isuzu/Subaru Amount as of such date, (v) the Series 2005-2 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the aggregate Net Book Value of all Vehicles manufactured by Hyundai and leased under the Leases as of such date over the Series 2005-2 Maximum Hyundai Amount as of such date, (vi) the Series 2005-2 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the aggregate Net Book Value of all Vehicles

manufactured by Kia and leased under the Leases as of such date over the Series 2005-2 Maximum Kia Amount as of such date, (vii) the Series 2005-2 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the aggregate Net Book Value of all Vehicles manufactured by Suzuki and leased under the Leases as of such date over the Series 2005-2 Maximum Suzuki Amount as of such date, (viii) the Series 2005-2 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the Specified States Amount as of such date over the Series 2005-2 Maximum Specified States Amount as of such date and (ix) the Series 2005-2 AESOP I Operating Lease Vehicle Percentage as of the immediately preceding Business Day of the excess, if any, of the Non-Eligible Manufacturer Amount as of such date over the Series 2005-2 Maximum Non-Eligible Manufacturer Amount as of such date.

“Series 2005-2 Standard & Poor’s Highest Enhanced Vehicle Percentage” means, as of any date of determination, a fraction, expressed as a percentage, (a) the numerator of which is the sum, without duplication, of (i) the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease that are manufactured by either of the Standard & Poor’s Specified Non-Investment Grade Manufacturers as of such date, (ii) the excess, if any, of (A) the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease that are manufactured by a Standard & Poor’s Non-Investment Grade Manufacturer other than a Standard & Poor’s Specified Non-Investment Grade Manufacturer, as of such date over (B) 30.00% of the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease as of such date, (iii) the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease that are manufactured by a Bankrupt Manufacturer and (iv) the Series 2005-2 Standard & Poor’s Kia/Hyundai Highest Enhanced Vehicle Percentage Amount on such day and (b) the denominator of which is the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease as of such date.

“Series 2005-2 Standard & Poor’s Lowest Enhanced Vehicle Percentage” means, as of any date of determination, a fraction, expressed as a percentage, (a) the numerator of which is an amount equal to (X) the sum, without duplication, of (1) the aggregate Net Book Value of all Program Vehicles leased under the AESOP I Operating Lease that are manufactured by Eligible Program Manufacturers having long-term senior unsecured debt ratings of “BBB+” or higher from Standard & Poor’s as of such date, (2) so long as any Eligible Non-Program Manufacturer has a long-term senior unsecured debt rating of “BBB+” or higher from Standard & Poor’s and no Manufacturer Event of Default has occurred and is continuing with respect to such Eligible Non-Program Manufacturer, the aggregate Net Book Value of all Non-Program Vehicles leased under the AESOP I Operating Lease manufactured by each such Eligible Non-Program Manufacturer that are subject to a Manufacturer Program and remain eligible for repurchase thereunder as of such date and (3) the lesser of (A) the sum of (x) if as of such date any Eligible Program Manufacturer has a long-term senior unsecured debt rating of “BBB” from Standard & Poor’s, the aggregate Net Book Value of all Program Vehicles leased under the AESOP I Operating Lease manufactured by each such Eligible Program Manufacturer as of such

date and (y) if as of such date any Eligible Non-Program Manufacturer has a long-term senior unsecured debt rating of “BBB” from Standard & Poor’s and no Manufacturer Event of Default has occurred and is continuing with respect to such Eligible Non-Program Manufacturer, the aggregate Net Book Value of all Non-Program Vehicles leased under the AESOP I Operating Lease manufactured by each such Eligible Non-Program Manufacturer that are subject to a Manufacturer Program and remain eligible for repurchase thereunder as of such date and (B) 10% of the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease as of such date minus (Y) the Series 2005-2 Standard & Poor’s Kia/Hyundai Lowest Enhanced Vehicle Percentage Adjustment Amount as of such date and (b) the denominator of which is the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease as of such date.

2. Each of the following defined terms are hereby added, in appropriate alphabetical order, to Article I(b) of the Series 2005-2 Supplement:

“Series 2002-2 Supplement” means, the Amended and Restated Series 2002-2 Supplement, dated as of November 22, 2002, as amended, modified or supplemented from time to time, among ABRCF, ABCR, as administrator, JPMorgan Chase Bank, N.A. (formerly known as JPMorgan Chase Bank), as administrative agent, the CP Conduit Purchasers, Funding Agents and APA Banks named therein, and The Bank of New York Mellon Trust Company, N.A. (as successor in interest to The Bank of New York), as trustee and as agent for the benefit of the Series 2002-2 Noteholders, to the Base Indenture.

“Series 2002-3 Supplement” means, the Series 2002-3 Supplement, dated as of September 12, 2002, as amended, modified or supplemented from time to time, among ABRCF, ABCR, as administrator, Park Avenue Receivables Corporation, as CP Conduit Purchaser, JPMorgan Chase Bank, N.A. (formerly known as JPMorgan Chase Bank), as Funding Agent and an APA Bank, and The Bank of New York Mellon Trust Company, N.A. (as successor in interest to The Bank of New York), as trustee and as agent for the benefit of the Series 2002-3 Noteholders, to the Base Indenture.

“Series 2005-4 Supplement” means, the Series 2005-4 Supplement, dated as of June 1, 2005, as amended, modified or supplemented from time to time, between ABRCF and The Bank of New York Mellon Trust Company, N.A. (as successor in interest to The Bank of New York), as trustee and as agent for the benefit of the Series 2005-4 Noteholders, to the Base Indenture.

“Series 2007-2 Supplement” means, the Series 2007-2 Supplement, dated as of June 6, 2007, as amended, modified or supplemented from time to time, between ABRCF and The Bank of New York Mellon Trust Company, N.A. (as successor in interest to The Bank of New York Trust Company, N.A.), as trustee and as agent for the benefit of the Series 2007-2 Noteholders, to the Base Indenture.

“Series 2008-1 Supplement” means, the Series 2008-1 Supplement, dated as of February 15, 2008, as amended, modified or supplemented from time to time, among ABRCF, ABCR, as administrator, JPMorgan Chase Bank, N.A., as administrative agent, the CP Conduit Purchasers, Funding Agents and APA Banks named therein, and The Bank of New York Mellon Trust Company, N.A. (as successor in interest to The Bank of New York Trust Company, N.A.), as trustee and as agent for the benefit of the Series 2008-1 Noteholders, to the Base Indenture.

“Series 2005-2 Maximum Hyundai Amount” means, as of any day, with respect to Hyundai, an amount equal to 20% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day.

“Series 2005-2 Maximum Individual Isuzu/Subaru Amount” means, as of any day, with respect to Isuzu or Subaru, individually, an amount equal to 5% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day.

“Series 2005-2 Maximum Kia Amount” means, as of any day, with respect to Kia, an amount equal to 10% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day.

“Series 2005-2 Maximum Suzuki Amount” means, as of any day, with respect to Suzuki, an amount equal to 7.5% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day.

“Series 2005-2 Standard & Poor’s Kia/Hyundai Highest Enhanced Vehicle Percentage Amount” means, as of any day, the sum, without duplication, of (i) the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease that are manufactured by Hyundai in excess of 15% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day, (ii) the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease that are manufactured by Kia in excess of 7.5% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day, and (iii) the aggregate Net Book Value of all Vehicles leased under the AESOP I Operating Lease that are manufactured by Hyundai and Kia, in the aggregate in excess of 20% of the aggregate Net Book Value of all Vehicles leased under the Leases on such day.

“Series 2005-2 Standard & Poor’s Kia/Hyundai Lowest Enhanced Vehicle Percentage Adjustment Amount” means, (i) as of any date of determination on which either Kia or Hyundai has a long-term senior unsecured debt rating of at least “BBB” from Standard & Poor’s, the sum without duplication of the Net Book Values as of such date of each Vehicle manufactured by Kia and/or Hyundai (as the case may be) that is included both in (x) the calculation of the Series 2005-2 Standard & Poor’s Kia/Hyundai Highest Enhanced Vehicle Percentage Amount on such date and (y) the calculation of subclause (a)(X) of the definition of Series 2005-2 Standard & Poor’s Lowest Enhanced Vehicle Percentage on such date and (ii) as of any other date, zero.

3. Each of the following defined terms, as set forth in Article I(b) of the Series 2005-2 Supplement, is hereby deleted in its entirety: “Series 2005-2 Maximum Aggregate Kia/Isuzu/Subaru/Hyundai/Suzuki Amount”, “Series 2005-2 Maximum Individual Hyundai/Suzuki Amount” and “Series 2005-2 Maximum Individual Kia/Isuzu/Subaru Amount.”

4. Article 6 of the Series 2005-2 Supplement is hereby amended by adding the following clauses as Section 6.23 and Section 6.24:

“Section 6.23 Capitalized Cost Covenant. ABRCF hereby agrees that (i) it shall not permit the aggregate Capitalized Cost for all Vehicles purchased in any model year that are not subject to a Manufacturer Program to exceed 85% of the aggregate MSRP (Manufacturer Suggested Retail Price) of all such Vehicles and (ii) it shall not modify its buying patterns or purchasing criteria with respect to the Vehicles where the primary purpose of such modification is compliance with clause (i) of this covenant.”

“Section 6.24 Concentration Limit Representation. ABRCF hereby represents that, as of November 11, 2008, (i) the concentration limits with respect to Kia, Hyundai, Suzuki, Mitsubishi, Subaru and Isuzu in the Series 2005-2 Supplement are identical in all material respects to the concentration limits for such Manufacturers in each of the Series 2002-2 Supplement, the Series 2002-3 Supplement, the Series 2007-2 Supplement and the Series 2008-1 Supplement, (ii) the treatment of Hyundai and Kia Vehicles in the Series 2005-2 Standard & Poor’s Highest Enhancement Percentage is identical in all material respects to the treatment of Hyundai and Kia Vehicles in the Standard & Poor’s Highest Enhancement Percentage in the Series 2002-2 Supplement, the Series 2002-3 Supplement, the Series 2007-2 Supplement and the Series 2008-1 Supplement and (ii) the Series 2005-2 Maximum Non-Program Vehicle Percentage is identical in all material respects to the Maximum Non-Program Vehicle Percentage with respect to each of the Series 2002-2 Supplement, the Series 2002-3 Supplement, the Series 2005-4 Supplement, the Series 2007-2 Supplement and the Series 2008-1 Supplement.”

5. This Amendment is limited as specified and, except as expressly stated herein, shall not constitute a modification, acceptance or waiver of rights under, or of any other provision of, the Series 2005-2 Supplement.

6. This Amendment shall become effective as of the date (the “Amendment Date”) on which each of the following has occurred: (i) each of the parties hereto shall have executed and delivered this Amendment to the Trustee, (ii) the Rating Agency Consent Condition shall have been satisfied with respect to each outstanding Series of Notes and each Enhancement Provider pursuant to the Base Indenture and related Supplements, (iii) all certificates and opinions of counsel required under the Base Indenture or otherwise deliverable with respect to this Amendment shall have been delivered to the Trustee and the Surety Provider, (iv) the Surety Provider, as the Requisite Noteholder and third-party beneficiary of this Amendment, shall have executed the Consent Letter consenting hereto and (v) a majority of the Managers of ABRCF has approved this Amendment.

7. From and after the Amendment Date, (i) all references to the Series 2005-2 Supplement shall be deemed to be references to the Series 2005-2 Supplement as amended hereby, (ii) the Series 2005-2 Supplement, as amended hereby, shall remain in full force and effect and (iii) this Amendment shall constitute a Transaction Document as defined in the Insurance Agreement.

8. ABRCF hereby reaffirms that each of the representations and warranties of ABRCF in the Transaction Documents that are qualified by materiality or by material adverse effect are true and correct, and that each of the representations and warranties of ABRCF in the Transaction Documents that are not qualified by materiality or by material adverse effect are true and correct in all material respects, in each case on and as of the date hereof as if made on the date hereof.

9. ABRCF hereby confirms that it is in compliance in all material respects with its covenants in the Transaction Documents, and that the Surety Provider is an express third-party beneficiary of this Amendment and ABRCF’s reaffirmations and confirmations set forth herein.

10. This Amendment may be executed in separate counterparts by the parties hereto, each of which when so executed and delivered shall be an original but all of which shall together constitute one and the same instrument.

11. THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES HEREUNDER SHALL BE CONSTRUED IN ACCORDANCE WITH AND GOVERNED BY THE LAWS OF THE STATE OF NEW YORK.

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