AMENDMENT ONE to the MERCK & CO., INC. 1996 NON-EMPLOYEE DIRECTORS STOCKOPTION PLAN (Amended April 27, 1999)

Exhibit 10.12

AMENDMENT ONE

to the

MERCK & CO., INC.

1996 NON-EMPLOYEE DIRECTORS STOCK OPTION PLAN

(Amended April 27, 1999)

WHEREAS, pursuant to and upon consummation of the Agreement and Plan of Merger, dated March 8, 2009, as amended, by and among, Merck & Co., Inc. (“Merck”), Schering-Plough Corporation, SP Merger Subsidiary One, Inc., and SP Merger Subsidiary Two, Inc. (the “Transactions”), Schering-Plough Corporation will change its name to Merck & Co. Inc., (“Parent”) and Merck will change its name to Merck Sharp & Dohme Corp. (“MSD”), and will become a wholly-owned subsidiary of Parent;

WHEREAS, under Section 11 of the Merck 1999 Non-Employee Directors Stock Option Plan (the “1996 Directors Plan”), the Board of Directors of Merck may from time to time amend the terms of the 1996 Directors Plan and desires to amend, contingent on and effective upon the consummation of the Transactions, the 1996 Directors Plan to reflect, (i) the change to the stock underlying any stock option awards granted under the 1996 Directors Plan that remain outstanding as of the closing date of the Transactions from the common stock of Merck, par value $0.01 per share to the common stock of Parent, par value $0.50 per share; and (ii) other technical changes that are considered necessary for the proper continuation of such outstanding equity grants and the 1996 Directors Plan in light of the Transactions; provided however, for the avoidance of any doubt, if the Transactions is not consummated, all amendments as set forth herein shall be null and void;

NOW, THEREFORE, BE IT

RESOLVED, that in consideration of the premises, the 1996 Directors Plan is hereby amended contingent on and as of the consummation of the Transactions as follows:

1. The first sentence of the Preamble of the 1996 Directors Plan shall be deleted and replaced with the following two sentences:

The 1996 Non-Employee Directors Stock Option Plan (the “Plan”), effective January 1, 1996, was established to attract, retain and compensate for service as members of the Board of Directors of Merck & Co., Inc. (“Merck”). The Plan is amended, effective as of the Closing Date, as such term is defined in Section 1.2 of the Agreement and Plan of Merger dated as of March 8, 2009, by and among Merck, Schering Plough Corporation, SP Merger Subsidiary One, Inc., and SP Merger Subsidiary Two, Inc. (the “Transactions”), whereby Schering Plough Corporation will be renamed Merck & Co., Inc. (“Parent”) and Merck will be renamed Merck Sharp and Dohme Corp. (“MSD”) and will be a wholly-owned subsidiary of Parent. On and after the Closing Date, references in the Plan to the “Company” shall be read to refer to the “Parent.”

2. Section 1 of the 1996 Directors Plan shall be amended to add the following sentence at the end of Section 1:

Effective as of the Closing Date, only those Non-Employee Directors who served as Non-Employee Directors of Merck prior to the Transactions and who participated in the Plan prior to the Transactions will be participants in the Plan following the Transactions with respect to any options granted prior to the Transactions that remain outstanding as of the Closing Date.

3. Section 2 of the 1996 Directors Plan shall be amended by adding the following sentence to the end of Section 2:

Effective as of the Closing Date, each NQSO that was granted pursuant to the Plan prior to the Transactions and remained outstanding as of the Closing Date, will be exercisable for a share of common stock of the Parent, par value $0.50 per share (“Parent Common Stock”) in lieu of a share of common stock of Merck, par value $0.01 per share. For all purposes of the Plan, effective on the Closing Date, all references to “Merck Common Stock” or the “Company’s Common Stock” in the Plan will refer to “Parent Common Stock.”

4. The first sentence of Section 11 of the 1996 Directors Plan shall be amended to read:

This Plan shall be administered by the Board of Directors of Parent.

5. All references in the 1996 Directors Plan to the “Board of Directors” or “Board” shall refer to the Board of Directors of Parent.

6. This amendment is effective as of the Closing Date of the Transactions.

MERCK & CO., INC.

1996 NON-EMPLOYEE DIRECTORS

STOCK OPTION PLAN

(Amended April 27, 1999)

The 1996 Non-Employee Directors Stock Option Plan (the “Plan”) is established to attract, retain and compensate for service as members of the Board of Directors of Merck & Co., Inc. (the “Company”) highly qualified individuals who are not current or former employees of the Company and to enable them to increase their ownership in the Company’s Common Stock. The Plan will be beneficial to the Company and its stockholders since it will allow these directors to have a greater personal financial stake in the Company through the ownership of Company stock, in addition to underscoring their common interest with stockholders in increasing the value of the Company stock longer term.

1. Eligibility

All members of the Company’s Board of Directors who are not current or former employees of the Company or any of its subsidiaries (“Non-Employee Directors”) are eligible to participate in this Plan.

2. Options

Only nonqualified stock options (“NQSOs”) may be granted under this Plan.

3. Shares Available

a) Number of Shares Available: There is hereby reserved for issuance under this Plan 450,000 shares of Merck Common Stock, par value $0.01 per share, which may be authorized but unissued shares, treasury shares, or shares purchased on the open market.

b) Recapitalization Adjustment: In the event of a reorganization, recapitalization, stock split, stock dividend, combination of shares, , consolidation, rights offering, or any other change in the corporate structure or shares of the Company, adjustments in the number and kind of shares authorized by this Plan, in the number and kind of shares covered by, and in the option price of outstanding NQSOs under this Plan shall be made if, and in the same manner as, such adjustments are made to NQSOs issued under the Company’s then current Incentive Stock Plan.

4. Annual Grant of Nonqualified Stock Options

Each year on the first Friday following the Company’s Annual Meeting of Stockholders, each individual elected, reelected or continuing as a Non-Employee Director shall automatically receive NQSOs covering five thousand (5,000) shares of Merck Common Stock. Notwithstanding the foregoing, if, on that first Friday, the General Counsel of the Company determines, in her/his sole discretion, that the Company is in possession of material, undisclosed information about the Company, then the annual grant of NQSOs to Non-Employee Directors

shall be suspended until the second day after public dissemination of such information and the price, exercisability date and option period shall then be determined by reference to such later date. If Merck Common Stock is not traded on the New York StockExchange on any date a grant would otherwise be awarded, then the grant shall be made the next day thereafter that Merck Common Stock is so traded.

5. Option Price

The price of the NQSO shall be the closing price on the date of the grant of the Company’s Common Stock as quoted on the composite tape of the New York Stock Exchange.

6. Option Period

A NQSO granted under this Plan shall become exercisable five years after date of grant and shall expire ten years after date of grant (“Option Period”).

7. Payment

The NQSO price shall be paid in cash in U.S. dollars at the time the NQSO is exercised.

8. Cessation of Service

Upon cessation of service as a Non-Employee Director (for reasons other than retirement or death), only those NQSOs immediately exercisable at the date of cessation of service shall be exercisable by the grantee. Such NQSOs must be exercised within ninety days of cessation of service (but in no event after the expiration of the Option Period) or they shall be forfeited.

9. Retirement

If a grantee ceases service as a Non-Employee Director and is at least age 65 with ten or more years of service or age 70 with five or more years of service, then any of his/her outstanding NQSOs shall continue to become exercisable. All outstanding NQSOs must be exercised by the earlier of (i) sixty months following the date of such cessation of service or (ii) the expiration of the Option Period, or such NQSOs shall be forfeited.

10. Death

Upon the death of a grantee, those NQSOs which had been held for at least twelve months at date of death shall become immediately exercisable upon death. The NQSOs which become exercisable upon the date of death and those NQSOs which were exercisable on the date of death may be exercised by the grantee’s legal representatives or heirs by the earlier of (i) thirty-six months from the date of death or (ii) the expiration of the Option Period; if not exercised by the earlier of (i) or (ii), such NQSOs shall be forfeited.

11. Administration and Amendment of the Plan

This Plan shall be administered by the Board of Directors of Merck & Co., Inc. This Plan may be terminated or amended by the Board of Directors as it deems advisable. However, an amendment revising the price, date of exercisability, option period of, or amount of shares under a NQSO shall not be made more frequently than every six months unless necessary to comply with applicable laws or regulations. No amendment may revoke or alter in a manner unfavorable to the grantees any NQSOs then outstanding, nor may the Board amend this Plan without stockholder approval where the absence of such approval would cause the Plan to fail to comply with Rule 16b-3 under the Securities Exchange Act of 1934 (the “Act”), or any other requirement of applicable law or regulation. A NQSO may not be granted under this Plan after December 31, 2000 but NQSOs granted prior to that date shall continue to become exercisable and may be exercised according to their terms.

12. Transferability

Except as set forth in this section, the NQSOs granted under this Plan shall not be exercisable during the grantee’s lifetime by anyone other than the grantee, the grantee’s legal guardian or the grantee’s legal representative, and shall not be transferable other than by will or by the laws of descent and distribution. NQSOs granted under this Plan shall be transferable during a grantee’s lifetime only in accordance with the following provisions:

The grantee may only transfer an NQSO while serving as a Non-Employee Director of the Company or within one year of ceasing service as a Non-Employee Director due to retirement as defined in Section 9. The NQSO may be transferred only to the grantee’s spouse, children (including adopted children and stepchildren) and grandchildren (collectively, “Family Members”), to one or more trusts for the benefit of Family Members or, at the discretion of the Board of Directors, to one or more partnerships where the grantee and his Family Members are the only partners, in accordance with the rules set forth in this section. The grantee shall not receive any payment or other consideration for such transfer (except that if the transfer is to a partnership, the grantee shall be permitted to receive an interest in the partnership in for the transfer).

Any NQSO transferred in accordance with this section shall continue to be subject to the same terms and conditions in the hands of the transferee as were applicable to such NQSO prior to the transfer, except that the grantee’s right to transfer such NQSO in accordance with this section shall not apply to the transferee. However, if the transferee is a natural person, upon the transferee’s death, the NQSO privileges may be exercised by the legal representatives or beneficiaries of the transferee within the exercise periods otherwise applicable to the NQSO.

Any purported transfer of an NQSO under this section shall not be effective unless, prior to such transfer, the grantee has (1) met the minimum stock ownership target then in place for Directors of the Company, (2) notified the Company of the transferee’s name and address, the number of shares under the Option to be transferred, and the grant date and exercise price of such shares, and (3) demonstrated, if requested by the Board of Directors, that the proposed transferee

qualifies as a permitted transferee under the rules set forth in this section. In addition, the transferee must sign an agreement that he or she is bound by the rules and regulations the Plans and by the same insider trading restrictions that apply to the grantee. No transfer shall be effective unless the Company has in effect a registration statement filed under the Securities Act of 1933 covering the securities to be acquired by the transferee upon exercise of the NQSO, or the General Counsel of Merck & Co., Inc. has determined that registration of such shares is not necessary.

13. Compliance with SEC Regulations

It is the Company’s intent that the Plan comply in all respects with Rule 16b-3 of the Act, and any regulations promulgated thereunder. If any provision of this Plan is later found not to be in compliance with the Rule, the provision shall be deemed null and void. All grants and exercises of NQSOs under this Plan shall be executed in accordance with the requirements of Section 16 of the Act, as amended, and any regulations promulgated thereunder.

14. Miscellaneous

Except as provided in this Plan, no Non-Employee Director shall have any claim or right to be granted a NQSO under this Plan. Neither the Plan nor any action thereunder shall be construed as giving any director any right be retained in the service of the Company.

15. Effective Date

This Plan shall be effective April 23, 1996 or such later date as stockholder approval is obtained.