IDERA PHARMACEUTICALS, INC. AMENDMENT NO. 1 TO CONVERTIBLE PREFERRED STOCK AND WARRANT PURCHASE AGREEMENT

Exhibit 10.4

IDERA PHARMACEUTICALS, INC.

AMENDMENT NO. 1 TO CONVERTIBLE PREFERRED STOCK AND WARRANT PURCHASE AGREEMENT

This Amendment No. 1 to Convertible Preferred Stock and Warrant Purchase Agreement (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 “Purchaser”).

WHEREAS, the Company and Purchaser entered into that certain Convertible Preferred Stock and Warrant Purchase Agreement, dated as of November 4, 2011 (the “Purchase Agreement”), by and between the Company and Purchaser;

WHEREAS, the Company and the Purchaser desire to amend certain sections of the Purchase Agreement, as set forth below;

WHEREAS, pursuant to Section 7.4 of the Purchase Agreement, any amendment of the Purchase Agreement requires the written consent of the Company and the Purchasers holding a majority of the shares of Series D Preferred Stock (as defined in the Purchase Agreement) then outstanding;

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 Purchaser hereby agree as follows:

1. Section 5.2 of the Purchase Agreement is hereby terminated and of no further force and effect.

2. The Company hereby agrees that the purchase by certain affiliates of the Purchaser of securities of the Company pursuant to that certain Convertible Preferred Stock and Warrant Purchase Agreement, dated November 9, 2012, among the Company and the Purchasers named therein shall not be in violation of Section 5.7 of the Purchase Agreement.

3. Section 5.8 of the Purchase Agreement is hereby amended by deleting such Section in its entirety from the Purchase Agreement and inserting the following in lieu thereof:

“5.8 Voting Rights.

(A) Each Purchaser hereby agrees that, to the extent that and for so long as the total number of shares of Common Stock beneficially owned by the Purchaser and its affiliates and any other persons whose beneficial ownership of Common Stock would be aggregated with the Purchaser for purposes of Section 13(d) of the Exchange Act exceeds 19.99% (prior to the date that 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 Purchase Agreement, dated November 9, 2012, among the Company and the Purchasers named therein (the “SERIES E PURCHASE AGREEMENT”)) or 25%

(effective upon the date that the stockholders of the Company approve the Nasdaq Proposal), in any election of directors and in any other vote to be taken by the stockholders of the Company (whether taken at an annual or special meeting of stockholders or by written action), it and its affiliates will vote any Excess Shares (as defined below) held in the same manner as and in the same proportion to the votes cast by the other holders of the Company’s Common Stock or other voting securities.

(B) Each Purchaser hereby constitutes and appoints as the proxies of the party and hereby grants a power of attorney to the officers of the Company, and each of them, with full power of substitution, with respect to clause (A) above, and hereby authorizes each of them to represent and to vote, if and only if the Purchaser (i) fails to vote or (ii) attempts to vote (whether by proxy, in person or by written consent), in a manner which is inconsistent with the terms of clause (A), all of such Purchaser’s Excess Shares in accordance with the terms of clause (A). Each of the proxy and power of attorney granted pursuant to the immediately preceding sentence is given in consideration of the agreements and covenants of the Company and the parties in connection with the transactions contemplated by this Agreement and, as such, each is coupled with an interest and shall be irrevocable unless and until this Agreement terminates or expires. Each Purchaser hereby revokes any and all previous proxies or powers of attorney with respect to the Excess Shares and shall not hereafter, unless and until this Agreement terminates or expires, purport to grant any other proxy or power of attorney with respect to any of such Excess Shares, deposit any of such Excess Shares into a voting trust or enter into any agreement (other than this Agreement), arrangement or understanding with any person, directly or indirectly, to vote, grant any proxy or give instructions with respect to the voting of any of such Excess Shares, in each case, with respect to clause (A) above.

(C) Each Purchaser agrees to refrain from exercising (and hereby affirmatively waives) any dissenters’ rights or rights of appraisal under applicable law at any time with respect to any Sale of the Corporation (as defined in the Corporation’s Certificate of Designations, Preferences and Rights of Series E Preferred Stock) to the extent such Sale of the Corporation has been approved by the Company’s Board of Directors.

(D) For purposes of this Section 5.8, “Excess Shares” means for any Purchaser the number of shares of voting stock held by the Purchaser and its affiliates equal to (i) the total number of shares of Common Stock held by the Purchaser and its affiliates (including Conversion Shares and shares of Common Stock issuable upon conversion of other series of Preferred Stock held by the Purchaser and its affiliates), less (ii) 19.99% (prior to the date that the stockholders of the Company approve the Nasdaq Proposal) or 25% (effective upon the date that the stockholders of the Company approve the Nasdaq Proposal) of the total number of shares of Common Stock then outstanding (including all Conversion Shares and all other shares of Common Stock then issuable upon conversion of other series of Preferred Stock then outstanding).”

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4. Section 6.1 of the Purchase Agreement is hereby amended by deleting such Section in its entirety from the Purchase Agreement and inserting the following in lieu thereof:

“6.1 Restrictions on Transferability.

(A) Subject to Section 6.1(B), the Securities shall not be sold, transferred, assigned or hypothecated unless (i) there is an effective registration statement under the Securities Act covering such Securities, (ii) the sale is made in accordance with Rule 144 under the Securities Act, or (iii) the Company receives an opinion of counsel for the holder of the Securities reasonably satisfactory to the Company stating that such sale, transfer, assignment or hypothecation is exempt from the registration requirements of the Securities Act, and each such case upon all other conditions specified in this Section 6.1. Notwithstanding the provisions of the preceding sentence, no such registration statement or opinion of counsel shall be required for any transfer of any Securities by a Purchaser that is a partnership, a limited liability company or a corporation to (a) a partner of such partnership, a member of such limited liability company or a stockholder of such corporation, (b) an entity that controls, or is controlled by, or is under common control with such partnership, limited liability company or corporation, or (c) the estate of any such partner, member or stockholder (collectively, clauses (a) through (c) the “PERMITTED TRANSFEREES”); provided, that in each of the foregoing cases the proposed transferee of the Securities held by the Purchaser agrees in writing to take and hold such Securities subject to the provisions and upon the conditions specified in this Section 6.

(B) Notwithstanding anything to the contrary set forth in this Agreement, without the prior written consent of the Company, the Purchaser may not sell or transfer any Securities to a person, entity or group (within the meaning of Section 13(d) of the Exchange Act) in one or more transactions if such sale or transfer would, in the aggregate, result in the transfer to such person, entity or group Securities representing, or exercisable for stock of the Company representing, more than 5% of the then outstanding combined voting power of the outstanding securities of the Company (other than a sale or transfer to a Permitted Transferee who agrees in writing to be bound by such restrictions or in connection with a resale of such Securities in connection with an underwritten public offering that has been approved by the Board).

(C) Any transfer not made in compliance with the requirements of this Section 6.1 shall be null and void ab initio, shall not be recorded on the books of the Company or its transfer agent and shall not be recognized by the Company. Each Purchaser acknowledges and agrees that any breach of this Section 6.1 by a Purchaser would result in substantial harm to the Company and its stockholders for which monetary damages alone could not adequately compensate. Therefore, each Purchaser unconditionally and irrevocably agrees that the Company shall be entitled to seek protective orders, injunctive relief and other remedies available at law or in equity (including without limitation, seeking specific performance or the rescission of purchases, sales and other transfers of Securities not made in compliance with this Section 6.1.”

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5. Section 7.6 of the Purchase Agreement is hereby amended by deleting the phrase “Commonwealth of Massachusetts” and inserting the phrase “State of Delaware” in lieu thereof.

6. The Purchase Agreement, as amended by this Agreement, together with any other writings referred to in the Purchase Agreement 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.

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

8. 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.

9. 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 Convertible Preferred Stock and Warrant Purchase Agreement has been executed by the parties hereto as of the day and year first above written.

Amendment No. 1 to Convertible Preferred Stock and Warrant Purchase Agreement

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

Amendment No. 1 to Convertible Preferred Stock and Warrant Purchase Agreement