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:

 

  A. Amendment to the Agreement.

 

  1. The definition of “Equity Investment” in Section 1.01 of the Agreement is
hereby removed and replaced in its entirety with the following:

“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.

 

  2. Section 4.02(a) of the Agreement is hereby removed and replaced in its
entirety with the following:

“(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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  B. Binding Effect. This Amendment shall be legally binding and enforceable in
accordance with its terms, and shall be binding upon and inure to the benefit of
each of the undersigned’s heirs, successors and assigns.

[Signature Page Follows]

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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.

 

GIVEN UNDER THE COMMON SEAL

of ELAN CORPORATION, PLC

in the presence of:

     

/s/ Robert A. Ingram

   Signature of Authorised Signatory   

/s/ William F. Daniel

   Signature of Director/Secretary

GIVEN UNDER THE COMMON SEAL

of PROTHENA CORPORATION PLC

in the presence of:

     

/s/ Shane Cooke

  

Signature of Director

Shane Cooke

  

/s/ Tara Nickerson

  

Signature of Director/Secretary

Tara Nickerson