INFINITY PHARMACEUTICALS, INC. SECOND AMENDMENT TO RIGHTS AGREEMENT

Exhibit 4.1

INFINITY PHARMACEUTICALS, INC.

SECOND AMENDMENT TO RIGHTS AGREEMENT

This Second Amendment to Rights Agreement (this “Amendment”) is made as of November 19, 2008 between Infinity Pharmaceuticals, Inc., a Delaware corporation (formerly known as Discovery Partners International, Inc. (the “Company”)), and American Stock Transfer & Trust Company, LLC (formerly known as American Stock Transfer & Trust Company, as rights agent (the “Rights Agent”)).

WHEREAS, the Company and the Rights Agent entered into that certain Rights Agreement, dated as of February 13, 2003 (the “Rights Agreement”);

WHEREAS, the Company and the Rights Agent entered into that certain First Amendment of Rights Agreement dated as of April 10, 2006 (the “First Amendment”); and

WHEREAS, the Company and the Rights Agent wish to further amend the Rights Agreement, as amended by the First Amendment, as provided below.

NOW, THEREFORE, in consideration of the foregoing premises and the mutual covenants and conditions set forth below, and for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties to this Amendment hereby agree as follows:

1. Further Amendment of Rights Agreement.

1.1 That the definition of “Acquiring Person” set forth in Section 1(a) of the Rights Agreement be amended to read in its entirety as follows:

“Acquiring Person” shall mean any Person (as such term is hereinafter defined) who or which, together with all Affiliates and Associates (as such terms are hereinafter defined) of such Person, shall be the Beneficial Owner (as such term is hereinafter defined) of 15% or more of the shares of Common Stock of the Company then outstanding, but shall not include:

(1) the Company, any Subsidiary (as such term is hereinafter defined) of the Company, any employee benefit plan of the Company or any Subsidiary of the Company, or any entity holding shares of Common Stock of the Company for or pursuant to the terms of any such plan;

(2) the Purchasers (as such term is defined in that certain Securities Purchase Agreement, dated as of November 19, 2008, between the Company and the Purchasers named therein (the “Securities Purchase Agreement”)) and any of their Associated Companies (as defined below) (such Purchasers and their Associated Companies referred to herein collectively as the “Investment Group”) solely with respect to:

(A) An aggregate of (a) four million (4,000,000) shares of Common Stock representing the Initial Closing Shares (as defined below) and (b) two million (2,000,000) shares of Common Stock representing the Second Closing Shares (as defined below), in each case issued to the Purchasers pursuant to Sections 1(a) and 1(b), respectively, of the Securities Purchase Agreement;

(B) Up to an additional two million four hundred thousand (2,400,000) shares of Common Stock acquired by the Investment Group after the Second Closing Date (as defined below) in open market purchase transactions and/or privately negotiated acquisitions, other than pursuant to a Make Whole Acquisition (as defined in paragraph (D) below);

(C) Up to an additional six million (6,000,000) shares of Common Stock issuable upon exercise of the Warrants (as defined below) acquired by the members of the Investment Group pursuant to Section 1(b) of the Securities Purchase Agreement; and

(D) the Investment Group solely as a result of the exercise of their rights described in the following sentence to make one or more Make Whole Acquisitions. If on or after the Initial Closing Date (as defined below) the Company issues shares of Common Stock or issues Common Stock upon conversion or exercise of securities convertible or exercisable into shares of Common Stock other than pursuant to the Securities Purchase Agreement, such additional shares of Common Stock as may be acquired in open market purchases and/or privately negotiated acquisitions from time to time by members of the Investment Group as may be required to maintain the Investment Group’s Common Stock ownership percentage as set forth in Schedule 5(b) of the Securities Purchase Agreement (each a “Make Whole Acquisition”); provided that any such Make Whole Acquisition only occurs during the period commencing upon the Second Closing Date and ending on the earlier to occur of (x) December 31, 2013 and (y) the termination of the Strategic Alliance Agreements, as such term is defined in the Securities Purchase Agreement;

Subject to Section 1.1(4) below and notwithstanding anything contained in clauses (A) through (D) above, in no event shall the total amount of Common Stock beneficially owned by the members of the Investment Group exceed 33.3% of the Company’s then current Fully-Diluted Common Outstanding (as defined below).

(3) any Person who, alone or together with all Affiliates and Associates of such Person, was, at the time of the announcement by the Company of the declaration by its board of directors on February 13, 2003 of the dividend distribution of the Rights, the Beneficial Owner of 15% or more of the Common Stock of the Company then outstanding, unless and until such time as such Person or any Affiliate or Associate of such Person becomes the Beneficial Owner of any additional shares of Common Stock (other than as a result of a stock dividend, stock split or similar transaction effected by the Company in which all holders of Common Stock are treated equally); and

(4) any Person that the board of directors of the Company in good faith determines has become an “Acquiring Person” inadvertently, and such Person has divested or divests as promptly as practicable a sufficient number of shares of Common Stock so that such Person would no longer be an “Acquiring Person” hereunder. Furthermore, notwithstanding anything stated in Section 1.1 of this Amendment to the contrary, no Person shall become an “Acquiring Person” as a result of (i) an acquisition of Common Stock by the Company or (ii) in the case of

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the Investment Group, the exercise or cancellation of outstanding securities that are exercisable, convertible or exchangeable for shares of Common Stock (including but not limited to outstanding options and warrants to purchase Common Stock), which, as a result of reducing the number of shares of Fully-Diluted Common Outstanding, increases the proportionate number of shares beneficially owned by such person to 15% or more of the shares of Common Stock then outstanding (or, in the case of the Investment Group, more than 33.3% of the Company’s then current Fully-Diluted Common Outstanding); provided, however, that if a Person shall become the Beneficial Owner of 15% or more of the shares of Common Stock then outstanding (or, in the case of the Investment Group, more than 33.3% of the Company’s then current Fully-Diluted Common Outstanding) as a result of (i) the acquisition of shares of Common Stock by the Company (as described in the immediately preceding clause) or (ii) in the case of the Investment Group, the exercise or cancellation of outstanding securities that are exercisable, convertible or exchangeable for shares of Common Stock (including but not limited to outstanding options and warrants to purchase Common Stock) and shall thereafter become the Beneficial Owner of any additional shares of Common Stock (other than as a result of a stock dividend, stock split or similar transaction effected by the Company in which all holders of Common Stock are treated equally), then such Person shall be deemed to be an “Acquiring Person” hereunder.

All references herein to numbers of shares of Common Stock or Fully-Diluted Common Outstanding shall be subject to adjustment for any stock split, reverse stock split, stock dividend, reclassification, recapitalization or other similar change to the Common Stock.

For purposes of this definition of “Acquiring Person,” (i) “Fully-Diluted Common Outstanding” shall mean the number of then issued and outstanding shares of Common Stock together with all shares of Common Stock issuable upon the exercise or conversion, as applicable, of all exercisable or convertible securities of the Company then outstanding and (ii) the terms “Associated Companies,” “Initial Closing Date,” “Initial Closing Shares,” “Second Closing Date,” “Second Closing Shares” and “Warrants” shall have the meanings given them in the Securities Purchase Agreement.

1.2 That Section 35 of the Right Agreement, as amended, be deleted.

2. No Other Amendment. Except as provided in this Amendment, the Rights Agreement, as amended, shall remain in full force and effect without any modification. The Company will not enter into any further amendment to the Rights Agreement that would allow a claim to be made or enforced by the Company that the Investment Group is an “Acquiring Person” for purposes of the Rights Agreement or otherwise deemed to trigger the provisions of the Rights Agreement provided that the Investment Group is in compliance with Section 1.1 of this Amendment. By executing below, the Company certifies that this Amendment has been executed and delivered in compliance with the terms of Section 27 of the Rights Agreement. This Amendment shall become effective when executed and delivered by the Company and the Rights Agent as provided in Section 27 of the Rights Agreement and shall be irrevocable.

3. Counterparts. This Amendment may be executed in counterparts, each of which shall constitute an original and all of which, when taken together, shall constitute one agreement.

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The foregoing Amendment is hereby executed as of the date first above written.

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