Exhibit 3.4

LIMITED LIABILITY COMPANY AGREEMENT

OF

AMYLIN PHARMACEUTICALS, LLC

Dated as of August 8, 2012

LIMITED LIABILITY COMPANY AGREEMENT

OF

AMYLIN PHARMACEUTICALS, LLC

This Limited Liability Company Agreement (this “Agreement”) of Amylin Pharmaceuticals, LLC is entered into by BMS Holdco, Inc., a Delaware corporation, as sole member (the “Managing Member”).

The Managing Member hereby forms a limited liability company pursuant to and in accordance with the Delaware Limited Liability Company Act (6 Del.C. § 18-101, et seq.), as amended from time to time (the “Act”), and hereby agrees as follows:

1. Name. The name of the limited liability company formed hereby is Amylin Pharmaceuticals, LLC (the “Company”).

2. Purpose. The Company is formed for the object and purpose of, and the nature of the business to be conducted and promoted by the Company is, engaging in any lawful act or activity for which limited liability companies may be formed under the Act and engaging in any and all activities necessary or incidental to the foregoing.

3. Members. The name and mailing address of the Managing Member is as follows:

4. Powers. The Managing Member of the Company shall manage the Company in accordance with this Agreement. The actions of the Managing Member taken in such capacity and in accordance with this Agreement shall bind the Company.

i. The Managing Member shall have full, exclusive and complete discretion to manage and control the business and affairs of the Company, to make all decisions affecting the business, operations and affairs of the Company and to take all such actions as it deems necessary or appropriate to accomplish the purpose of the Company as set forth herein. Subject to the provisions of this Agreement, the Managing Member shall have general and active management of the business and operations of the Company. In addition, the Managing Member shall have such other powers and duties as may be prescribed by the Managing Member or this Agreement. Such duties may be delegated by the Managing Member to officers, agents or employees of the Company as the Managing Member may deem appropriate from time to time.

ii. The Managing Member may, from time to time, designate one or more persons to be officers of the Company. No officer need be a member of the Company. Any officers so designated will have such authority and perform such duties as the Managing Member may, from time to time, delegate to them. The Managing Member may assign titles to particular officers, including, without limitation, chairman, chief executive officer, president, vice

president, chief operating officer, secretary, assistant secretary, treasurer and assistant treasurer. Each officer will hold office until his or her successor will be duly designated and will qualify or until his or her death or until he or she will resign or will have been removed. Any number of offices may be held by the same person. The salaries or other compensation, if any, of the officers and agents of the Company will be fixed from time to time by the Managing Member or by any officer acting within his or her authority. Any officer may be removed as such, either with or without cause, by the Managing Member whenever in his, her or its judgment the best interests of the Company will be served thereby. Any vacancy occurring in any office of the Company may be filled by the Managing Member. The names of the initial officers of the Company, and their respective titles, are set forth on the attached Schedule 1.

5. Tax Elections. The Taxable Year shall be the Fiscal Year. The Managing Member will upon request supply the information necessary to give proper effect to such election.

6. Dissolution. The Company shall dissolve, and its affairs shall be wound up upon the first to occur of the following (a) the written consent of the Managing Member; or (b) the death, retirement, resignation, expulsion, insolvency, bankruptcy or dissolution of the Managing Member or the occurrence of any other event which terminates the continued membership of a the Managing Member in the Company.

7. Liability of the Members. The Managing Member shall not have any liability for the obligations or liabilities of the Company except to the extent provided in the Act.

8. Indemnification of Members, Officers and Others.

i. Each person who was or is made a party or is threatened to be made a party to or is involved in any action, suit or proceeding, whether civil, criminal, administrative or investigative (hereinafter a “proceeding”), by reason of the fact that he or a person of whom he is the legal representative, is or was a member or officer (or was a former director), of the Company or is or was serving at the request of the Company as a director, officer, employee, fiduciary, or agent of another corporation or of a partnership, joint venture, trust or other enterprise, including service with respect to employee benefit plans, whether the basis of such proceeding is alleged action in an official capacity as a member, officer, former director, employee, fiduciary or agent or in any other capacity while serving as a member, officer, former director, employee, fiduciary or agent, shall be indemnified and held harmless by the Company to the fullest extent which it is empowered to do so by the Act, as the same exists or may hereafter be amended (but, in the case of any such amendment, only to the extent that such amendment permits the Company to provide broader indemnification rights than said law permitted the Company to provide prior to such amendment) against all expense, liability and loss (including attorneys’ fees actually and reasonably incurred by such person in connection with such proceeding and such indemnification shall inure to the benefit of his or her heirs, executors and administrators; provided, however, that, except as provided in Section 8(ii) hereof, the Company shall indemnify any such person seeking indemnification in connection with a proceeding initiated by such person or any proceeding by such person against the Company or its members, officers, former directors, employees or other agents only if (i) such proceeding was authorized by the Managing Member of the Company, (ii) such indemnification is provided by

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the Company, in its sole discretion, pursuant to the powers vested in the Company under the Act or (iii) such indemnification is expressly required to be made by law. The right to indemnification conferred in this Section 8 shall be a contract right and, subject to Sections 8(ii) and 8(v) hereof, shall include the right to be paid by the Company the expenses incurred in defending any such proceeding in advance of its final disposition. The Company may, by action of its Managing Member, provide indemnification to employees and agents of the Company with the same scope and effect as the foregoing indemnification of members and officers.

ii. Any indemnification of a member, officer or former member, officer or director of the Company under Section 8(i) or advance of expenses under Section 8(v) shall be made promptly, and in any event within 30 days, upon the written request of the member, officer or former member, officer or director. If a determination by the Company that the member, officer or former member, officer or director is entitled to indemnification pursuant to this Section 8 is required, and the Company fails to respond within sixty days to a written request for indemnity, the Company shall be deemed to have approved the request. If the Company denies a written request for indemnification or advancing of expenses, in whole or in part, or if payment in full pursuant to such request is not made within 30 days, the right to indemnification or advances as granted by this Section 9 shall be enforceable by the member or officer in any court of competent jurisdiction. Such person’s costs and expenses incurred in connection with successfully establishing his or her right to indemnification, in whole or in part, in any such action shall also be indemnified by the Company. It shall be a defense to any such action (other than an action brought to enforce a claim for expenses incurred in defending any proceeding in advance of its final disposition where the required undertaking, if any, has been tendered to the Company) that the claimant has not met the standards of conduct which make it permissible under the Act for the Company to indemnify the claimant for the amount claimed, but the burden of such defense shall be on the Company. Neither the failure of the Company (including its Managing Member, independent legal counsel, or its stockholders) to have made a determination prior to the commencement of such action that indemnification of the claimant is proper in the circumstances because he or she has met the applicable standard of conduct set forth in the Act, nor an actual determination by the Company (including its Managing Member, independent legal counsel, or its stockholders) that the claimant has not met such applicable standard of conduct, shall be a defense to the action or create a presumption that the claimant has not met the applicable standard of conduct.

iii. For purposes of any determination under this Agreement, the member, officer or former member, officer or director shall be deemed to have acted in good faith and in a manner he reasonably believed to be in or not opposed to the best interests of the Company, and, with respect to any criminal action or proceeding, to have had no reasonable cause to believe that his conduct was unlawful, if his action is based on information, opinions, reports and statements, including financial statements and other financial data in each case prepared or presented by: (i) one or more officers or employees of the Company whom the member, officer or former member, officer or director believed to be reliable and competent in the matters presented, (ii) counsel, independent accountants or other persons as to matters which the member, officer or former member, officer or director believed to be within such person’s professional competence and (iii) with respect to a former director, a committee of the former board of directors upon which the director did not serve, as to matters within such committee’s designated authority, which committee the director believes to merit confidence; so long as, in each case, the member,

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officer or former member, officer or director acts without knowledge that would cause such reliance to be unwarranted. The termination of any proceeding by judgment, order, settlement, conviction or upon a plea of nolo contendere or its equivalent shall not, of itself, create a presumption that the person did not act in good faith and in a manner which he reasonably believed to be in or not opposed to the best interests of the Company, and, with respect to any criminal proceeding, that he had reasonable cause to believe that his conduct was unlawful. The provisions of this Section 8(iii) shall not be deemed to be exclusive or to limit in any way the circumstances in which a person may be deemed to have met the applicable standard of conduct set forth by the Act.

iv. The rights to indemnification and the payment of expenses incurred in defending a proceeding in advance of its final disposition conferred in this Section 8 shall not be exclusive of any other right which any person may have or hereafter acquire under any statute, provision of the Certificate of Formation, operating agreement, vote of members or otherwise.

v. The Company may purchase and maintain insurance on its own behalf and on behalf of any person who is a member, officer, former director, employee, fiduciary, or agent of the corporation or was serving at the request of the corporation as a director, officer, employee or agent of another corporation, partnership, joint venture, trust or other enterprise against any liability asserted against him or her and incurred by him or her in any such capacity, whether or not the Company would have the power to indemnify such person against such liability under this Section 8.

vi. Expenses incurred by any person described in Section 8(i) in defending a proceeding shall be paid by the Company in advance of such proceeding’s final disposition upon receipt of an undertaking by or on behalf of the member, officer or former director to repay such amount if it shall ultimately be determined that he or she is not entitled to be indemnified by the Company. Notwithstanding the foregoing, no advance shall be made by the Company if a determination is reasonably and promptly made (i) by the Managing Member, or (ii) if the Managing Member so directs, by independent legal counsel in a written opinion, that the facts known to the decision making party at the time such determination is made demonstrate clearly and convincingly that such person acted in bad faith or in a manner that such person did not believe to be in or not opposed to the best interests of the Company.

vii. Persons who are not covered by the foregoing provisions of this Section 8 and who are or were employees or agents of the Company, or who are or were serving at the request of the Company as employees or agents of another corporation, partnership, joint venture, trust or other enterprise, may be indemnified to the extent authorized at any time or from time to time by the Managing Member.

viii. The provisions of this Section 8 shall be deemed to be a contract right between the Company and the Managing Member and each officer who serves in any such capacity at any time while this Section 8 and the relevant provisions of the Act or other applicable law are in effect, and any repeal or modification of this Section 8 or any such law shall only be prospective and shall not affect the rights under this Agreement in effect at the time of the alleged occurrence of any action or omission to act that is the cause of any proceeding against any agent of the Company.

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ix. For purposes of this Section 8, references to “the Company” shall include, in addition to the resulting company, any constituent company (including any constituent of a constituent) absorbed in a consolidation or merger which, if its separate existence had continued, would have had power and authority to indemnify its members, directors, officers, and employees or agents, so that any person who is or was a member, director, officer, employee or agent of such constituent company, or is or was serving at the request of such constituent company as a director, officer, employee or agent of another corporation, partnership, joint venture, trust or other enterprise, shall stand in the same position under this Section 8 with respect to the resulting or surviving company as he or she would have with respect to such constituent corporation if its separate existence had continued.

x. If this Agreement or any portion hereof shall be invalidated on any ground by any court of competent jurisdiction, then the Company shall nevertheless indemnify each member, officer or former member, officer or director to the full extent not prohibited by any applicable portion of this Agreement that shall not have been invalidated, or by any other applicable law.

10. Governing Law. This Agreement shall be governed by, and construed under, the laws of the State of Delaware, all rights and remedies being governed by said laws.

11. Uncertificated. The Company will remain uncertificated for purposes of Article 8 of the Uniform Commercial Code, and will not take any action to treat the equity interests thereof as “securities” under or for purposes of Article 8 of the Uniform Commercial Code.

*        *        *         *

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IN WITNESS WHEREOF, the undersigned, intending to be legally bound, has duly executed this Limited Liability Company Agreement of Amylin Pharmaceuticals, LLC as of the 8th day of August 2012.

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Schedule 1

Initial Officers

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