AMENDMENT TO THE AUTONATION, INC. 2007 NON-EMPLOYEE DIRECTOR STOCK OPTION PLAN

Exhibit 10.4

AMENDMENT TO THE AUTONATION, INC.

2007 NON-EMPLOYEE DIRECTOR STOCK OPTION PLAN

WHEREAS, the Board of Directors (the “Board”) of AutoNation, Inc. (the “Company”) has determined that it is in the best interest of the Company that the AutoNation, Inc. 2007 Non-Employee Director Stock Option Plan (the “Plan”) be amended to provide for quarterly stock option grants; and

WHEREAS, the Board has the authority under Section 12 of the Plan to amend the Plan.

NOW, THEREFORE, pursuant to Section 12 thereof, the Plan is hereby amended as set forth below:

1. The first paragraph of Section 5 of the Plan is hereby amended in its entirety to read as follows:

AUTOMATIC GRANTING OF OPTIONS. Commencing with the first trading day of March 2011, on the first trading day of each March, June, September and December while the Plan is in effect, each individual who is at the time serving as a Non-Employee Director shall receive an automatic grant of an Option to purchase 5,000 shares of Common Stock. The foregoing dates are herein referred to individually as an “Automatic Grant Date” and collectively as “Automatic Grant Dates” and the Non-Employee Directors receiving Options are herein referred to individually as an “Optionee” and collectively as “Optionees.” Options granted under the Plan are not intended to be treated as incentive stock options as defined in Section 422 of the Internal Revenue Code of 1986, as amended (the “Code”). For purposes of this Plan, the term “trading day” shall mean a day on which the New York Stock Exchange or the principal U.S. stock exchange upon the Company’s common stock is listed is open for trading.

2. The first sentence of Section 6 of the Plan is hereby amended in its entirety to read as follows:

The price per share payable upon exercise of an Option (“Exercise Price”) shall be the composite closing price of a share of Common Stock on the New York Stock Exchange or the principal U.S. stock exchange upon which the Company’s Common Stock is listed (the “Closing Price”) on the Automatic Grant Date.

3. The second sentence of Section 9 of the Plan is hereby amended in its entirety to read as follows:

Should an Optionee cease to be an outside member of the Board of Directors of the Company because of Retirement, death or permanent and total disability (as that term is defined in Section 22(e)(3) of the Code, as now in effect or as subsequently amended), the Option may be exercised in full by the Optionee or, if he or she is

not living, by his or her heirs, legatees, or legal representative, as the case may be, during its specified term prior to three years after the date of Retirement, death or permanent and total disability (without regard to whether such Optionee subsequently resumes service as an outside member of the Board), but in no event after the expiration date of the Option.

4. Effect on Plan. Except as expressly amended hereby, the Plan shall remain in full force and effect.

5. Effective Date. The effective date of this Amendment shall be the date on which it is adopted by the Board.