Merck Sharp & Dohme Corp., formerly known as Merck & Co., Inc. and Merck & Co., Inc., formerly known as Schering-Plough Corporation, as Guarantor to U.S. BANK TRUST NATIONAL ASSOCIATION,

Exhibit 4.3

Merck Sharp & Dohme Corp., formerly known as Merck & Co., Inc.

and Merck & Co., Inc., formerly known as Schering-Plough Corporation, as Guarantor

to

U.S. BANK TRUST NATIONAL ASSOCIATION,

as Trustee

(as successor to Morgan Guaranty Trust Company of New York)

Second Supplemental Indenture

Dated as of November 3, 2009

to

Indenture

Dated as of April 1, 1991

SUPPLEMENTAL INDENTURE, dated as of November 3, 2009 (the “Supplemental Indenture”) among Merck Sharp & Dohme Corp., formerly known as Merck & Co., Inc., a corporation duly organized and existing under the laws of the State of New Jersey (the “Company”), having its principal office at One Merck Drive, Whitehouse Station, New Jersey 08889, Merck & Co., Inc., formerly known as Schering-Plough Corporation, a corporation duly organized and existing under the laws of the State of New Jersey, having its principal office at One Merck Drive, Whitehouse Station, New Jersey 08889 (the “Guarantor”), and U.S. BANK TRUST NATIONAL ASSOCIATION, a national banking association duly organized and existing under the laws of the United States (as successor to Morgan Guaranty Trust Company of New York), as Trustee (the “Trustee”).

R E C I T A L S

WHEREAS, the Company has heretofore executed and delivered to the Trustee an Indenture, dated as of April 1, 1991, as supplemented by the First Supplemental Indenture dated as of October 1, 1997 (herein called the “Indenture”) between the Company and the Trustee. All terms used in this Supplemental Indenture which are defined in the Indenture shall have the same meanings assigned to them in the Indenture.

Whereas, there have previously been issued and are now outstanding under the Indenture, the following series of Securities: $250,000,000 aggregate principal amount of the Company’s 5?% Notes due 2011, $1,250,000,000 aggregate principal amount of the Company’s 1.875% Notes due 2011, $500,000,000 aggregate principal amount of the Company’s 4.375% Notes due 2013, $1,000,000,000 aggregate principal amount of the Company’s 4.75% Notes due 2015, $1,000,000,000 aggregate principal amount of the Company’s 4.000% Notes due 2015, $1,250,000,000 aggregate principal amount of the Company’s 5.000% Notes due 2019, $250,000,000 aggregate principal amount of the Company’s 6.3% debentures due 2026, $500,000,000 aggregate principal amount of the Company’s 6.4% debentures due 2028, $500,000,000 aggregate principal amount of the Company’s 5.95% debentures due 2028, $500,000,000 aggregate principal amount of the Company’s 5¾% Notes due 2036, $112,947,000 aggregate principal amount of the Company’s 5.76% Notes due 2037, $750,000,000 aggregate principal amount of the Company’s 5.850% Notes due 2039, $35,000,000 aggregate principal amount of the Company’s floating rate notes due November 27, 2040, $46,000,000 aggregate principal amount of the Company’s floating rate notes due December 21, 2040, $25,000,000 aggregate principal amount of the Company’s floating rate notes due December 27, 2040, $26,000,000 aggregate principal amount of the Company’s floating rate notes due February 6, 2041, $34,670,000 aggregate principal amount of the Company’s floating rate notes due June 21, 2041, $25,000,000 aggregate principal amount of the Company’s floating rate notes due July 18, 2041, $43,053,000 aggregate principal amount of the Company’s floating rate notes due December 21, 2041, $30,000,000 aggregate principal amount of the Company’s floating rate notes due November 28, 2041, $75,522,000 aggregate principal amount of the Company’s floating rate notes due August 22, 2042, $68,514,000 aggregate principal amount of the Company’s floating rate notes due February 18, 2043, and $41,225,000 aggregate principal amount of the Company’s floating rate notes due February 12, 2044 (collectively, the “Notes”).

WHEREAS, the Guarantor has become the ultimate parent company of the Company and desires to add a covenant to fully and unconditionally guarantee all of the obligations of the Company under the Notes and the Indenture on the terms set forth herein promptly after the closing of the Merger (as defined below).

WHEREAS, Section 901(2) of the Indenture provides that, without the consent of any Holders, the Company, when authorized by a Board Resolution, and the Trustee, at

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any time and from time to time, may enter into one or more indentures supplemental thereto, in form satisfactory to the Trustee, to add to the covenants of the Company for the benefit of the Holders of all or any series of Securities (and if such covenants are to be for the benefit of less than all series of Securities, stating that such covenants are expressly being included solely for the benefit of such series) or to surrender any right or power conferred in the Indenture upon the Company.

WHEREAS, Section 901(9) of the Indenture provides that, without the consent of any Holders, the Company, when authorized by a Board Resolution, and the Trustee, at any time and from time to time, may enter into one or more indentures supplemental thereto, in form satisfactory to the Trustee, to cure any ambiguity, to correct or supplement any provision in the Indenture which may be defective or inconsistent with any other provision therein, or to make any other provisions with respect to matters or questions arising under the Indenture, provided that such action shall not adversely affect the interests of the Holders of Securities of any series in any material respect.

WHEREAS, the Company has delivered to the Trustee an Opinion of Counsel pursuant to Section 903 of the Indenture stating that the execution of this Supplemental Indenture is authorized or permitted by the Indenture.

WHEREAS, all things necessary to make this Supplemental Indenture a valid agreement of the Company and the Guarantor, in accordance with its terms, have been done.

NOW, THEREFORE, for and in consideration of the premises and the covenants contained in this Supplemental Indenture, the parties hereto hereby agree for the equal and proportionate benefit of all Holders of the Notes as follows:

SECTION 1. (a) For all purposes of this Supplemental Indenture:

(1) All references herein to Articles and Sections, unless otherwise specified, refer to the corresponding Articles and Sections of this Supplemental Indenture and, where so specified, to the Articles and Sections of the Indenture as supplemented by this Supplemental Indenture; and

(2) The terms “hereof”, “herein”, “hereby”, “hereto”, “hereunder” and “herewith” refer to this Supplemental Indenture.

(b) For all purposes of the Indenture and this Supplemental Indenture, with respect to the Notes, except as otherwise expressly provided or unless the context otherwise requires:

“Guarantee” means the guarantee of the Company’s obligations under the Notes of the applicable series and the Indenture by the Guarantor under this Supplemental Indenture.

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“Guaranteed Obligations” has the meaning specified in Section 3(a)(1) hereof.

“Guarantor” means the Person named as the “Guarantor” in the first paragraph of this Supplemental Indenture until a successor Person shall have become such pursuant to the applicable provisions of the Indenture, and thereafter “Guarantor” shall mean such successor Person.

SECTION 2: COVENANT TO GUARANTEE.

As a result of the closing of the merger of the Company with the Guarantor, the Guarantor covenants and agrees to execute and deliver to the Trustee a supplemental indenture pursuant to which the Guarantor will agree to fully and unconditionally guarantee, on a senior unsecured basis, all of the Company’s obligations under the Notes, with such Guarantee is to be automatically and unconditionally released and discharged if (1) at any time the Guarantor has no Debt outstanding and does not guarantee the Debt of any Subsidiary (other than the Notes), or (2) the Indenture has been satisfied and discharged in accordance with Section 401 of the Indenture.

SECTION 3: GUARANTEE.

(a) Guarantee.

(1) With respect to each series of Notes, the Guarantor hereby fully and unconditionally guarantees to each Holder of that series of Notes and to the Trustee and its successors and assigns (1) the full and punctual payment when due, whether at Maturity, by acceleration, by redemption or otherwise, of all obligations of the Company under the Indenture (including obligations to the Trustee) and the Notes of that series, whether for payment of principal of, or interest, premium, if any, on, the Notes of that series and all other monetary obligations of the Company under the Indenture and the Notes of that series and (2) the full and punctual performance within applicable grace periods of all other obligations of the Company whether for fees, expenses, indemnification or otherwise under the Indenture and the Notes of that series (all the foregoing being hereinafter collectively called the “Guaranteed Obligations” with respect to the Notes of that series). The Guarantor further agrees that the Guaranteed Obligations may be extended or renewed, in whole or in part, without notice or further assent from the Guarantor, and that the Guarantor shall remain bound under this Section 3 notwithstanding any extension or renewal of any Guaranteed Obligation.

(2) The Guarantor waives presentation to, demand of payment from and protest to the Company of any of the Guaranteed Obligations and also waives notice of protest for nonpayment. The Guarantor waives notice of any default under the Notes of each series or the Guaranteed Obligations with respect to each series of Notes. The obligations of the Guarantor hereunder shall not be affected by (1) the failure of any Holder or the Trustee to assert any claim or demand or to enforce any right or remedy against the Company or any other Person under the Indenture, the Notes or any other agreement or otherwise; (2) any extension or renewal of any thereof; (3) any rescission, waiver, amendment or modification of any of the terms or provisions of the Indenture, the Notes or any other agreement; (4) the release of any security held by any Holder or the Trustee for the Guaranteed Obligations or any of them; or (5) the failure of any Holder or Trustee to exercise any right or remedy against any other guarantor of the Guaranteed Obligations.

(3) The Guarantor hereby waives any right to which it may be entitled to have the assets of the Company first be used and depleted as payment of the

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Company’s or such Guarantor’s obligations hereunder prior to any amounts being claimed from or paid by the Guarantor hereunder. The Guarantor hereby waives any right to which it may be entitled to require that the Company be sued prior to an action being initiated against the Guarantor.

(4) The Guarantor further agrees that its Guarantee herein constitutes a guarantee of payment when due (and not a guarantee of collection) and waives any right to require that any resort be had by any Holder or the Trustee to any security held for payment of the Guaranteed Obligations.

(5) Except as expressly set forth in Section 3(d) of this Supplemental Indenture, the obligations of the Guarantor hereunder shall not be subject to any reduction, limitation, impairment or termination for any reason, including any claim of waiver, release, surrender, alteration or compromise, and shall not be subject to any defense of setoff, counterclaim, recoupment or termination whatsoever or by reason of the invalidity, illegality or unenforceability of the Guaranteed Obligations or otherwise. Without limiting the generality of the foregoing, the obligations of the Guarantor herein shall not be discharged or impaired or otherwise affected by the failure of any Holder or the Trustee to assert any claim or demand or to enforce any remedy under the Indenture, the Notes or any other agreement, by any waiver or modification of any thereof, by any default, failure or delay, willful or otherwise, in the performance of the obligations, or by any other act or thing or omission or delay to do any other act or thing which may or might in any manner or to any extent vary the risk of the Guarantor or would otherwise operate as a discharge of the Guarantor as a matter of law or equity.

(6) Except as expressly set forth in Section 3(d) of this Supplemental Indenture, the Guarantor agrees that its Guarantee of a particular series of Notes shall remain in full force and effect until payment in full of all the Guaranteed Obligations of that series of Notes. The Guarantor further agrees that its Guarantee herein of a particular series of Notes shall continue to be effective or be reinstated, as the case may be, if at any time payment, or any part thereof, of principal of or interest on any Guaranteed Obligation of that series of Notes is rescinded or must otherwise be restored by any Holder of that series of Notes or the Trustee upon the bankruptcy or reorganization of the Company or otherwise.

(7) In furtherance of the foregoing and not in limitation of any other right which any Holder or the Trustee has at law or in equity against the Guarantor by virtue hereof, upon the failure of the Company to pay the principal of or interest on any Guaranteed Obligation of a particular series of Notes when and as the same shall become due, whether at maturity, by acceleration, by redemption or otherwise, or to perform or comply with any other Guaranteed Obligation with respect to that series of Notes, the Guarantor, hereby promises to and shall, upon receipt of written demand by the Trustee, forthwith pay, or cause to be paid, in cash, to the Holders or the Trustee an amount equal to the sum of (1) the unpaid principal amount of such Guaranteed Obligations with respect to that series of Notes, (2) accrued and unpaid interest on

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such Guaranteed Obligations with respect to that series of Notes (but only to the extent not prohibited by law) and (3) all other monetary obligations of the Company to the Holders of that series of Notes and the Trustee.

(8) The Guarantor agrees that it shall not be entitled to any right of subrogation in relation to the Holders in respect of any Guaranteed Obligations of a particular series of Notes guaranteed hereby until payment in full of all Guaranteed Obligations with respect to that series of Notes. The Guarantor further agrees that, as between it, on the one hand, and the Holders of a particular series of Notes and the Trustee, on the other hand, (1) the maturity of the Guaranteed Obligations guaranteed hereby with respect to that series of Notes may be accelerated as provided in the Indenture for the purposes of the Guarantee herein, notwithstanding any stay, injunction or other prohibition preventing such acceleration in respect of the Guaranteed Obligations guaranteed hereby, and (2) in the event of any declaration of acceleration of such Guaranteed Obligations with respect to that series of Notes as provided in the Indenture, the Guaranteed Obligations with respect to that series of Notes (whether or not due and payable) shall forthwith become due and payable by the Guarantor for the purposes of this Section 3.

(9) The Guarantor also agrees to pay any and all costs and expenses (including reasonable attorneys’ fees and expenses) incurred by the Trustee or any Holder in enforcing any rights under this Section 3.

(10) Upon request of the Trustee, the Guarantor shall execute and deliver such further instruments and do such further acts as may be reasonably necessary or proper to carry out more effectively the purpose of the Indenture.

(b) No Waiver. Neither a failure nor a delay on the part of either the Trustee or the Holders of any series of Notes in exercising any right, power or privilege under this Section 3 shall operate as a waiver thereof, nor shall a single or partial exercise thereof preclude any other or further exercise of any right, power or privilege. The rights, remedies and benefits of the Trustee and the Holders of each series of Notes herein expressly specified are cumulative and not exclusive of any other rights, remedies or benefits which either may have under this Section 3 at law, in equity, by statute or otherwise.

(c) Modification. No modification, amendment or waiver of any provision of this Section 3, nor the consent to any departure by the Guarantor therefrom, shall in any event be effective unless the same shall be in writing and signed by the Trustee, and then such waiver or consent shall be effective only in the specific instance and for the purpose for which given. No notice to or demand on the Guarantor in any case shall entitle the Guarantor to any other or further notice or demand in the same, similar or other circumstances.

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(d) Release of Guarantor.

The Guarantor shall, upon the occurrence of either of the following events, be automatically and unconditionally released and discharged from all obligations under this Supplemental Indenture and its Guarantee of each series of the Notes and the Holders of each series of the Notes will be deemed to have consented to such release without any action required on the part of the Trustee or any Holder of the Notes if:

(i) at any time the Guarantor has no Debt outstanding and does not guarantee the Debt of any Subsidiary of the Guarantor (other than the Notes); or

(ii) the Indenture has been satisfied and discharged in accordance with Section 401 of the Indenture.

If the conditions to release contained in this Section 3(d) have been satisfied, the Trustee shall execute any documents reasonably requested by the Company or the Guarantor in order to evidence the release of the Guarantor from all of its obligations under the Guarantee and the Indenture. Notwithstanding the foregoing, any failure to execute such documents shall in no way affect the release of the Guarantor pursuant to this Section 3(d), which release shall be automatic and unconditional upon satisfaction of either of the conditions to release set forth in clause (i) or (ii) above.

(e) Limitation on Guarantor Liability. It is hereby agreed that the Guarantee of the Guarantor shall not constitute a fraudulent transfer, fraudulent conveyance or fraudulent obligation for purposes of any applicable Federal or State bankruptcy, insolvency or reorganization or other similar law, the Uniform Fraudulent Conveyance Act, the Uniform Fraudulent Transfer Act or any similar federal or state law to the extent applicable to the Guarantee. The obligations of the Guarantor shall be limited to the maximum amount which will, after giving effect to all other contingent and fixed liabilities of the Guarantor that are relevant under such laws, and after giving effect to any collections from, rights to receive contributions from or payments made by or on behalf of any other Guarantor in respect of the obligations of such other Guarantor under this Section 3 that are relevant under such laws, result in the obligations of the Guarantor under its Guarantee not constituting a fraudulent conveyance, fraudulent transfer or fraudulent obligation under federal or state law. Until such time as the Notes of any particular series are paid in full, the Guarantor, with respect to such series of Notes, hereby waives all rights of subrogation, whether arising by contract or operation of law (including, without limitation, any such right arising under federal bankruptcy law) or otherwise by reason of any payment by it pursuant to the provisions of this Section 3.

SECTION 4. If any provision hereof limits, qualifies or conflicts with another provision hereof which is required to be included in this Supplemental Indenture by any of the provisions of the Trust Indenture Act, such required provision shall control.

SECTION 5. In case any provision in this Supplemental Indenture shall be invalid, illegal or unenforceable, the validity, legality, and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

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SECTION 6. Nothing in this Supplemental Indenture, express or implied, shall give to any Person, other than the parties hereto and their successors under the Indenture and the Holders of the Notes of each series, any benefit or any legal or equitable right, remedy or claim under this Supplemental Indenture.

SECTION 7. This Supplemental Indenture supplements the Indenture and shall be a part and subject to all the terms thereof. Except as supplemented hereby, the Indenture shall continue in full force and effect.

SECTION 8. This Supplemental Indenture may be executed in any number of counterparts, each of which as so executed shall be deemed to be an original, but all such counterparts shall together constitute but one and the same instrument.

SECTION 9. This Supplemental Indenture shall be governed by and construed in accordance with the laws of the State of New York.

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IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed, and their respective corporate seals to be hereunder affixed and attested, all as of the day and year first above written.

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