AMENDMENT NO. 1 TO TAX MATTERS AGREEMENT

Exhibit 10.2

AMENDMENT NO. 1 TO TAX MATTERS AGREEMENT

THIS AMENDMENT NO. 1 TO TAX MATTERS AGREEMENT (this “Amendment”) is made and entered into as of June 25, 2013 by and between Elan Corporation, plc, an Irish public limited company (“Parent”), and Prothena Corporation plc, an Irish public limited company (“Prothena”).

Reference is made to the Tax Matters Agreement (the “Agreement”) dated as of December 20, 2012 by and between Parent and Prothena. Reference is also made to that certain representation letter (the “Prothena Representation Letter”) executed and delivered by Prothena on December 20, 2012 in connection with the delivery of certain legal opinions with respect to tax matters. Capitalized terms used herein but not defined shall have the meanings assigned to such terms in the Agreement.

WHEREAS, Section 7.06 of the Agreement provides that, if there is a conflict between any provision of the Agreement and a provision in another Transaction Document, including the Prothena Representation Letter, the provision of the Agreement will control, unless specifically provided otherwise in the Agreement or in the applicable Transaction Document.

WHEREAS, for the avoidance of doubt, Parent and Prothena wish to amend the Agreement pursuant to Section 7.07(a) of the Agreement to conform certain provisions of the Agreement and the Prothena Representation Letter.

NOW, THEREFORE, for good and valuable consideration, the receipt of which is hereby acknowledged, Parent and Prothena agree as follows:

“Equity Investment” means Prothena’s potential issuance(s) of common shares, ordinary shares, American Depositary Receipts, ADSs and/or preferred shares to investors after the Transactions for cash in an aggregate amount not to exceed US$ 300,000,000.

“(a) During the Restricted Period, (i) neither Parent nor any of its Affiliates (or any officers or directors acting on behalf of Parent or any of its subsidiaries, or any Person acting with the implicit or explicit permission of any such officers or directors) shall take or fail to take any action if such action (or the failure to take such action) would (x) be inconsistent with any covenant, representation or statement made by, Parent or any of its Affiliates in the Parent Representation Letter or in any Transaction Document, or (y) prevent, or be reasonably likely to prevent, the Transactions (or any portion thereof) from qualifying for Tax-Free Treatment; and (ii) none of Prothena or any of its Affiliates (or any officers or directors acting on behalf of Prothena or any of its subsidiaries, or any Person acting with the implicit or explicit permission of any such officers or directors) shall take or fail to take any action if such action (or the failure to take such action) would (x) be inconsistent with any covenant, representation or statement made by, Prothena or any of its Affiliates in the Prothena Representation Letter or in any Transaction Document, or (y) prevent, or be reasonably likely to prevent, the Transactions (or any portion thereof) from qualifying for Tax-Free Treatment. Notwithstanding anything to the contrary in this Agreement or the Prothena Representation Letter, no issuance of shares of Prothena Capital Stock that complies with Section 4.02(b)(v) of this Agreement shall be deemed to be inconsistent with or a breach of the Prothena Representation Letter, including but not limited to Section 14 of the Prothena Representation Letter, or this Agreement, including but not limited to this Section 4.02(a).”

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IN WITNESS whereof this Agreement has been duly executed as a deed by the parties to it on the date set out at the beginning of this Agreement.