IDERA PHARMACEUTICALS, INC. AMENDMENT NO. 1 TO COMMON STOCK PURCHASE WARRANT

Exhibit 10.5

IDERA PHARMACEUTICALS, INC.

AMENDMENT NO. 1 TO COMMON STOCK PURCHASE WARRANT

This Amendment No. 1 to Common Stock Purchase Warrant (this “Agreement”) is made as of November 9, 2012, by and between Idera Pharmaceuticals, Inc., a Delaware corporation (the “Company”), and Pillar Pharmaceuticals I, L.P. (the “Registered Holder”).

WHEREAS, the Company issued and sold to the Registered Holder that certain Common Stock Purchase Warrant, dated as of November 4, 2011 (the “Warrant”) pursuant to that certain Convertible Preferred Stock and Warrant Purchase Agreement, dated November 4, 2011, among the Company and the Purchasers named therein;

WHEREAS, the Company and the Registered Holder desire to amend certain sections of the Warrant, as set forth below;

WHEREAS, pursuant to Section 11 of the Warrant, any amendment of the Warrant requires the written consent signed by the Company and the Registered Holder;

NOW, THEREFORE, in consideration of the foregoing, and for other valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and the Registered Holder hereby agree as follows:

1. Section 1(e) of the Warrant is hereby amended by deleting subsection (e) thereof in its entirety and inserting the following new subsection (e) in lieu thereof:

“(e) Exercise Limitation. Notwithstanding anything to the contrary contained herein, the Company shall not effect any exercise of this Warrant and the Registered Holder shall not be entitled to exercise this Warrant for a number of Warrant Shares in excess of that number of Warrant Shares which, upon giving effect to such exercise, would cause (i) the aggregate number of shares of Common Stock beneficially owned by the Registered Holder and its affiliates and any other persons whose beneficial ownership of Common Stock would be aggregated with the Registered Holder’s for purposes of Section 13(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), to exceed 19.99% of the total number of issued and outstanding shares of Common Stock of the Company following such exercise, or (ii) the combined voting power of the securities of the Company beneficially owned by the Registered Holder and its affiliates and any other persons whose beneficial ownership of Common Stock would be aggregated with the holder’s for purposes of Section 13(d) of the Exchange Act to exceed 19.99% of the combined voting power of all of the securities of the Company then outstanding following such exercise, unless, in either case, the stockholders of the Company approve the Nasdaq Proposal (as defined by and in accordance with Section 5.11(B) of that certain Convertible Preferred Stock and Warrant, dated November 9, 2012, among the Company and the Purchasers named therein), in which case, the 19.99% limitation under clause (i) and clause (ii) of this Section 1(e) shall be increased, with respect to the Registered Holder, to 35% for purposes of both clause (i) and clause (ii) of this Section 1(e). For purposes of this Section 1(e), the aggregate number of shares of Common Stock or voting securities beneficially owned by the Registered Holder and its affiliates and any other persons whose beneficial ownership of Common Stock would be aggregated with the Registered Holder’s for purposes of Section 13(d) of the Exchange Act shall include the shares of Common Stock issuable upon the exercise of this Warrant with respect to which such determination is being made, but shall exclude the number of shares of Common Stock which would be issuable upon (i) exercise of the remaining unexercised and non-cancelled portion of this Warrant by the Registered Holder and (ii) exercise or conversion of the unexercised, non-converted or non-cancelled portion of any other securities of the Company that do not have voting power (including without limitation any securities of the Company which would entitle the holder thereof to acquire at any time Common Stock, including without limitation any debt, preferred stock, right, option, warrant or other instrument that is at any time convertible into or exercisable or exchangeable for, or otherwise entitles the holder thereof to receive, Common Stock), subject to a limitation on conversion or exercise analogous to the limitation contained herein beneficially owned by the Registered Holder or any of its affiliates and other persons whose beneficial ownership of Common Stock would be aggregated with the Registered Holder’s for purposes of Section 13(d) of the Exchange Act.”

2. Section 13 of the Warrant is hereby amended by deleting the phrase “Commonwealth of Massachusetts” and inserting the phrase “State of Delaware” in lieu thereof.

3. The Warrant, as amended by this Agreement, together with any other writings referred to in the Warrant or delivered pursuant thereto which form a part thereof, contain the entire agreement among the parties with respect to the subject matter thereof and amend, restate and supersede all prior and contemporaneous arrangements or understandings with respect thereto.

4. Upon the effectiveness of this Agreement, on and after the date hereof, each reference in the Warrant to “this Agreement,” “hereunder,” “hereof,” “herein” or words of like import shall mean and be a reference to the Warrant, as amended hereby. Except as specifically amended above, the Warrant shall remain in full force and effect and are hereby ratified and confirmed.

5. This Agreement shall be governed by and construed in accordance with the General Corporation Law of the State of Delaware as to matters within the scope thereof, and as to all other matters shall be governed by and construed in accordance with the internal laws of the State of Delaware, without regard to conflict of laws principles that would result in the application of any law other than the law of the State of Delaware.

6. This Agreement may be executed in any number of counterparts, and each such counterpart shall be deemed to be an original instrument, but all such counterparts together shall constitute but one agreement.

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IN WITNESS WHEREOF, this Amendment No. 1 to Common Stock Purchase Warrant has been executed by the parties hereto as of the day and year first above written.

Amendment No. 1 to Common Stock Purchase Warrant

IN WITNESS WHEREOF, this Amendment No. 1 to Common Stock Purchase Warrant has been executed by the parties hereto as of the day and year first above written.

Amendment No. 1 to Common Stock Purchase Warrant