SECOND AMENDMENT TO RIGHTS AGREEMENT

Exhibit 4.1

EXECUTION VERSION

SECOND AMENDMENT TO RIGHTS AGREEMENT

THIS SECOND AMENDMENT (this “Amendment”), dated as of April 5, 2011, to the Rights Agreement (the “Rights Agreement”), dated October 21, 2002, by and between INSPIRE PHARMACEUTICALS, INC., a Delaware corporation (the “Company”), and COMPUTERSHARE TRUST COMPANY, N.A., a national banking association, as Rights Agent (the “Rights Agent”), is being executed at the direction of the Company. Capitalized terms used in this Amendment and not otherwise defined herein shall have the meanings given them in the Rights Agreement.

WHEREAS, Section 27 of the Rights Agreement provides that, prior to the Distribution Date, the Company may supplement or amend the Rights Agreement, in any respect, without approval of any holders of Rights, by action of its Board of Directors;

WHEREAS, pursuant to Section 27 of the Rights Agreement, the Company has delivered to the Rights Agent a certificate signed by an appropriate officer of the Company which states that the proposed amendment of the Rights Agreement is in compliance with the terms of Section 27 of the Rights Agreement;

WHEREAS, the Company first amended the Rights Agreement (the “First Amendment”) on July 17, 2007 in contemplation of the Company and Warburg Pincus Private Equity IX, L.P. (“WP”) entering into a securities purchase agreement relating to the acquisition by WP of shares of Series A Exchangeable Preferred Stock;

WHEREAS, Merck & Co., Inc. (“Parent”), Monarch Transaction Corp. (“Merger Sub”) and the Company contemplate entering into an Agreement and Plan of Merger (the “Merger Agreement”) providing for, among other things, the (i) a cash tender offer (the “Offer”) by Merger Sub to purchase all of the issued and outstanding shares of the Company’s common stock, par value $0.001 per share (the “Company Common Stock”) and the associated preferred stock purchase rights, (ii) the grant by the Company to Merger Sub of the Top-Up Option (as defined in the Merger Agreement) and (iii) following the consummation of the Offer, the merger of Merger Sub with and into the Company (the “Merger”), in each case, on the terms and subject to the conditions set forth in the Merger Agreement; and

WHEREAS, the Company desires to amend the Rights Agreement for a second time, as set forth herein, to facilitate the transactions contemplated by the Merger Agreement.

NOW, THEREFORE, in accordance with the procedures for amendment of the Rights Agreement set forth in Section 27 thereof, and in consideration of the foregoing and the mutual agreements herein set forth, the parties hereto, intending to be legally bound, hereby agree as follows:

1. AMENDMENT TO SECTION 1.

(a) The definition of “ACQUIRING PERSON” in Section 1 of the Rights Agreement, as amended by the First Amendment, is hereby further amended by striking the “and” before (iii) in the definition of “ACQUIRING PERSON” and adding the following immediately after the final sentence of the definition:

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“…and

(vi) Notwithstanding anything in this Agreement to the contrary, none of Parent, Merger Sub or any of their respective Affiliates or Associates shall be or become an Acquiring Person by reason of, and the term “Acquiring Person” shall not include any of Parent, Merger Sub or any of their respective Affiliates or Associates, solely by reason of, (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments thereto), (ii) the commencement or public announcement of the Offer, (iii) the purchase of Common Stock pursuant to the Offer, (iv) the consummation or public announcement of the Merger and the other Transactions, (v) the exercise, or public announcement of the exercise, of the option to purchase shares of Common Stock (and the purchase of such shares of Common Stock) pursuant to Section 1.4 of the Merger Agreement (vi) the execution and entry into that certain Tender and Support Agreement to be entered into by and among Parent, Merger Sub and certain shareholders of the Company (each such event and any combination of the foregoing, an “EXEMPT EVENT”.

(b) The definition of “BENEFICIAL OWNER” in Section 1 of the Rights Agreement, as amended by the First Amendment, is hereby further amended by adding the following immediately after the final sentence of the definition:

“Notwithstanding anything in this Agreement to the contrary, none of Parent, Merger Sub or any of their respective Affiliates or Associates, either individually, collectively or in any combination, shall be deemed a Beneficial Owner of, or to Beneficially Own, any securities solely by virtue of, or as a result of, an Exempt Event.”

(a) Section 1 of the Rights Agreement, as amended by the First Amendment, shall be further amended by adding immediately after the definition of “EXCHANGE RATIO”:

“EXEMPT EVENT” shall have the meaning set forth in the definition of ACQUIRING PERSON.

(b) Section 1 of the Rights Agreement, as amended by the First Amendment, shall be further amended by adding immediately after the definition of “INVESTOR DESIGNEE”:

“MERGER” shall have the meaning ascribed to such term in the Merger Agreement.

(c) Section 1 of the Rights Agreement, as amended by the First Amendment, shall be further amended by adding immediately after the definition of “MERGER”:

“MERGER AGREEMENT” shall mean that certain Agreement and Plan of Merger by and among Parent, Merger Sub, and the Company, dated as of April 5, 2011 (as such agreement may be amended from time to time).

(d) Section 1 of the Rights Agreement, as amended by the First Amendment, shall be further amended by adding immediately after the definition of “MERGER AGREEMENT”:

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“MERGER SUB” shall mean Monarch Transaction Corp., Delaware corporation.

(e) Section 1 of the Rights Agreement, as amended by the First Amendment, shall be further amended by adding immediately after the definition of “NASDAQ”:

“OFFER” shall have the meaning ascribed to such term in the Merger Agreement.

(f) Section 1 of the Rights Agreement, as amended by the First Amendment, shall be further amended by adding immediately after the definition of “OFFER”:

“PARENT” shall mean Merck & Co., Inc., a New Jersey corporation.

(g) Section 1 of the Rights Agreement, as amended by the First Amendment, shall be further amended by adding immediately after the definition of “SUMMARY OF RIGHTS”:

“TOP-UP OPTION” shall have the meaning ascribed to such term in the Merger Agreement.

(h) Section 1 of the Rights Agreement, as amended by the First Amendment, shall be further amended by adding immediately after the definition of “TRADING DAY”:

“TRANSACTIONS” shall have the meaning ascribed to such term in the Merger Agreement.

2. AMENDMENT TO SECTION 3.

3. Clause (ii) of Section 3(a) of the Rights Agreement, as amended by the First Amendment, is hereby amended and restated in its entirety as follows:

“(ii) the Close of Business on the tenth Business Day (or such later date as may be determined by action of the Company’s Board of Directors prior to such time as any Person becomes an Acquiring Person and of which the Company will give the Rights Agent prompt written notice) after the date that a tender or exchange offer by any Person (other than the Company, any Subsidiary of the Company, any employee benefit plan of the Company or of any Subsidiary of the Company or of any Subsidiary of the Company or any entity holding shares of Common Stock for or pursuant to the terms of any such plan, and other than Parent, Merger Sub or any of their respective Affiliates or Associates if such commencement is in connection with an Exempt Event) is commenced within the meaning of Rule 14(d)-(4)(a) of the Exchange Act Regulations, if upon consummation thereof such Person would become an Acquiring Person (the earlier of (i) and (ii) above being the “DISTRIBUTION DATE”), (x) the Rights will be evidenced (subject to the provisions of Section 3(b)) by the certificates for shares of Common Stock of the Company registered in the names of the holders thereof (which certificates shall also be deemed to be Rights Certificates) and not by separate Rights Certificates, and (y) the right to receive Rights Certificates will be transferable only in connection with the transfer of shares of Common Stock of the Company.”

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4. AMENDMENT TO SECTION 7. Section 7(a) of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

“The registered holder of any Rights Certificate evidencing exercisable Rights may exercise the Rights evidenced thereby (except as otherwise provided in this Agreement) in whole or in part at any time after the Distribution Date upon surrender of the Rights Certificate, with the form of election to purchase and the related certification duly executed, to the Rights Agent at the office of the Rights Agent designated for such purpose, together with payment of the Purchase Price for each Right being exercised (as such amount may be reduced (including to zero) pursuant to Section 11(a)(iii)) and an amount equal to any applicable transfer tax required to be paid by the holder of such Rights Certificate in accordance with Section 9 in cash, or by certified check, wire transfer or bank draft payable to the order of the Company), at or prior to the earliest of (i) the Close of Business on the tenth (10th) anniversary of the Distribution Date (the “FINAL EXPIRATION DATE”), (ii) the time at which the Rights are redeemed as provided in Section 23 (the “REDEMPTION DATE”), (iii) the time at which such Rights are exchanged as provided in Section 24, and (iv) the time immediately prior to the Effective Time (as defined in the Merger Agreement), but only if the Effective Time shall occur (the earliest of (i), (ii), (iii) and (iv) being the “EXPIRATION DATE”).

5. AMENDMENT TO SECTION 18. Section 18 of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

“The Company agrees to pay to the Rights Agent reasonable compensation for all services rendered by it under this Agreement and, from time to time, on demand of the Rights Agent, its reasonable expenses and counsel fees and other disbursements incurred in the administration and execution of this Agreement and the exercise and performance of its duties hereunder. The Company also agrees to indemnify the Rights Agent for, and to hold it harmless against, any loss, liability, or expense, incurred without gross negligence or willful misconduct on the part of the Rights Agent, for any action taken, suffered or omitted by the Rights Agent in connection with the execution, acceptance and administration of this Agreement and the exercise and performance of its duties, including the costs and expenses of defending against and appealing any claim of liability in the premises. This indemnity shall survive the termination of this Agreement and the expiration of the Rights. The costs and expenses incurred in enforcing this right of indemnification shall be paid by the Company.

The Rights Agent may conclusively rely upon and shall be protected and shall incur no liability for, or in respect of any action taken, suffered or omitted by it in connection with, its administration of this Agreement and the exercise and performance of its duties hereunder in reliance upon any Rights Certificate or certificate for Units or for other securities of the Company, instrument of assignment or transfer, power of attorney, endorsement, affidavit, letter, notice, direction, consent, certificate, statement, or other paper or document believed by it to be genuine and to be signed, executed and, where necessary, verified or acknowledged, by the proper Person or Persons, or otherwise upon the advice of counsel as set forth in Section 20.”

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6. AMENDMENT TO SECTION 20. Section 20(c) of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

“The Rights Agent shall be liable hereunder to the Company and any other Person only for its own gross negligence or willful misconduct.”

7. AMENDMENT TO SECTION 21. Section 21 of the Rights Agreement is hereby amended by adding to the end of such Section the following sentence:

“In the event the transfer agency relationship in effect between the Company and the Rights Agent terminates, the Rights Agent will be deemed to have resigned automatically and be discharged from its duties under this Agreement as of the effective date of such termination, and the Company shall be responsible for sending any required notice.”

8. AMENDMENT TO SECTION 25. Section 25(a)(iv) of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

“(iv) to effect any consolidation or merger into or with any other Person (other than a Subsidiary of the Company in a transaction which complies with Section 11(o)), or to effect any sale or other transfer (or to permit one or more of its Subsidiaries to effect any sale or other transfer), in one or more transactions, of 50% or more of the assets or earning power of the Company and its Subsidiaries (taken as a whole) to, any other Person (in each case, other than any Exempt Event),”

9. ADDITION OF SECTION 35. The Rights Agreement is hereby amended to add a new Section 35 which shall read as follows:

“Section 35. EXCEPTION OF CERTAIN TRANSACTIONS. Notwithstanding any provision of this Agreement to the contrary, (i) none of Parent, Merger Sub or any of their Affiliates or Associates shall be deemed an Acquiring Person, (ii) none of a Distribution Date, a Share Acquisition Date, a Section 11(a)(ii) Event, a Section 11(a)(ii) Trigger Date, a Section 13 Event or a Triggering Event shall be deemed to occur or to have occurred and (iii) no holder of any Rights shall be entitled to exercise such Rights under, or be entitled to any rights under, the Agreement, including, without limitation, under Section 7 of the Agreement, in any such case solely reason of or in connection with the occurrence of an Exempt Event”

10. ADDITION OF SECTION 36. The Rights Agreement is hereby amended to add a new Section 36 which shall read as follows:

“Section 36. FORCE MAJEURE. Notwithstanding anything to the contrary contained herein, the Rights Agent shall not be liable for any delays or failures in performance resulting from acts beyond its reasonable control including, without limitation, acts of God, terrorist acts, shortage of supply, breakdowns or malfunctions, interruptions or malfunction of computer facilities, or loss of data due to power failures or mechanical difficulties with information storage or retrieval systems, labor difficulties, or civil unrest.”

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11. AMENDMENTS TO SUMMARY OF RIGHTS. Exhibit C (“Summary of Right to Purchase Preferred Stock”) of the Rights Agreement shall be deemed amended in a manner consistent with this Amendment.

12. BENEFITS OF THIS AGREEMENT. All the covenants and provisions of this Amendment by or for the benefit of the Company or the Rights Agent shall bind and inure to the benefit of their respective successors and assigns hereunder.

13. SEVERABILITY. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated; provided, however, that notwithstanding anything in this Amendment to the contrary, if any such term, provision, covenant or restriction is held by such court or authority to be invalid, void or unenforceable and the Board determines in its good faith judgment that severing the invalid language from this Amendment would adversely affect the purpose or effect of this Amendment and the right of redemption set forth in Section 23 of the Rights Agreement shall have expired, such right shall be reinstated and shall not expire until the tenth Business Day following the date of such determination by the Board.

14. GOVERNING LAW. This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of the State of Delaware applicable to contracts made and to be performed entirely within Delaware.

15. EFFECTIVENESS AND EFFECT OF AMENDMENT.

(a) This Amendment is effective as of April 5, 2011, immediately prior to the execution of the Merger Agreement.

(b) Except as specifically modified herein and by the First Amendment, the Rights Agreement shall not otherwise be supplemented or amended by virtue of this Amendment, but shall remain in full force and effect. The execution, delivery and effectiveness of this Amendment shall not, except as expressly provided herein, constitute a waiver or amendment of any provision of the Rights Agreement. Upon and after the effectiveness of this Amendment, each reference in the Rights Agreement to “this Agreement”, “hereunder”, “hereof” or words of like import referring to the Rights Agreement, and each reference in any other document to “the Rights Agreement”, “thereunder”, “thereof” or words of like import referring to the Rights Agreement, shall mean and be a reference to the Rights Agreement as modified hereby.

16. DESCRIPTIVE HEADINGS. Descriptive headings of the several sections of this Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

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17. COUNTERPARTS. This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument. A signature to this Agreement transmitted electronically shall have the same authority, effect, and enforceability as an original signature.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed and attested, all as of the day and year first above written.

[SIGNATURE PAGE TO RIGHTS AMENDMENT]