AMENDMENT NO. 4 TO RIGHTS AGREEMENT

Exhibit 10.4

AMENDMENT NO. 4 TO RIGHTS AGREEMENT

THIS AMENDMENT NO. 4 TO RIGHTS AGREEMENT (the “Amendment”) is made as of the 17 day of May, 2007, by and between BIOSITE INCORPORATED, a Delaware corporation (the “Company”), and AMERICAN STOCK TRANSFER & TRUST COMPANY, a New York banking corporation (the “Rights Agent”).

WHEREAS, the Company is entering into an Agreement and Plan of Merger (as the same may be amended from time to time, the “Merger Agreement”), among the Company, Inverness Medical Innovations, Inc., a Delaware corporation (“Parent”), and Inca Acquisition, Inc., a Delaware corporation and a wholly-owned subsidiary of Parent (“Purchaser”), pursuant to which Purchaser will: (i) make a tender offer to acquire all of the issued and outstanding shares of common stock of the Company, par value $0.01 per share (“Common Stock”), on the terms and subject to the conditions set forth in the Merger Agreement (such tender offer, as it may be amended from time to time, is referred to in this Amendment as the “Offer”), (ii) be granted an irrevocable option to acquire certain additional shares of Common Stock directly from the Company on the terms and subject to the conditions set forth in the Merger Agreement (the “Top-Up Option”), and (iii) after acquiring shares of common stock of the Company pursuant to the Offer (and, if applicable, the Top-Up Option), Purchaser will merge with and into the Company upon the terms and subject to the conditions set forth in the Merger Agreement;

WHEREAS, the Company and the Rights Agent (as successor Rights Agent to Fleet National Bank (f.k.a. BankBoston, N.A.)) are parties to that certain Rights Agreement dated October 22, 1997, as it was amended on December 9, 1999, July 18, 2001 and March 24, 2007 (the “Rights Agreement”);

WHEREAS, the Company desires to amend the Rights Agreement in connection with the execution and delivery of the Merger Agreement; and

WHEREAS, the Board of Directors of the Company has approved this Amendment and authorized its appropriate officers to execute and deliver the same to the Rights Agent.

NOW, THEREFORE, in accordance with the procedures for amendment of the Rights Agreement set forth in Section 27 thereof, and in consideration of the foregoing and the mutual agreements herein set forth, the parties hereby agree as follows:

1. Capitalized terms that are not otherwise defined herein shall have the meanings ascribed to them in the Rights Agreement.

2. The definition of “Acquiring Person” set forth in Section 1(a) of the Rights Agreement is amended by adding the following sentence to the end of that section:

“Notwithstanding the foregoing, no Person shall be or become an Acquiring Person by reason of (i) the execution and delivery of the Agreement and Plan of Merger, dated as of May 17, 2007, among Inverness Medical Innovations, Inc., a Delaware corporation (“Parent”), Inca Acquisition, Inc., a Delaware corporation and a wholly-owned subsidiary of Parent (“Purchaser”), and the Company (the “Merger Agreement”) or any amendment thereto, (ii) the

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purchase by Purchaser of Common Stock pursuant to (A) a tender offer to acquire all of the issued and outstanding Common Stock to be commenced by Purchaser pursuant to, and on the terms and subject to the conditions set forth in, the Merger Agreement (such tender offer, as it may be amended from time to time, is referred to in this Agreement as the “Offer”) or (B) an irrevocable option to acquire certain additional shares of Common Stock directly from the Company, granted by the Company to Purchaser on the terms and subject to the conditions set forth in the Merger Agreement (the “Top-Up Option”), (iii) the merger of Purchaser with and into the Company pursuant to, and on the terms and subject to the conditions set forth in, the Merger Agreement (the “Merger”), or (iv) the consummation of any other transaction contemplated by the Merger Agreement, as it may be amended from time to time.”

3. The definition of “Stock Acquisition Date” in Section l(i) of the Rights Agreement is hereby amended by adding the following sentence to the end of that section:

“Notwithstanding anything else set forth in this Agreement, a Stock Acquisition Date shall be deemed not to have occurred by reason of (i) the execution and delivery or amendment of the Merger Agreement, (ii) the purchase by Purchaser of Common Stock pursuant to the Offer (and, if applicable, the Top-Up Option), (iii) the Merger, or (iv) the consummation of any other transaction contemplated by the Merger Agreement, as it may be amended from time to time.”

4. Section 3(a) of the Rights Agreement is hereby amended by adding the following sentence to the end of that section:

“Notwithstanding anything else set forth in this Agreement, no Distribution Date shall be deemed to have occurred by reason of (i) the execution and delivery or amendment of the Merger Agreement, (ii) the purchase by Purchaser of Common Stock pursuant to the Offer (and, if applicable, the Top-Up Option), (iii) the Merger, or (iv) the consummation of any other transaction contemplated by the Merger Agreement, as it may be amended from time to time.”

5. Section 7(a)(i) of the Rights Agreement is hereby amended to delete the phrase “(the “Final Expiration Date”)” so that it shall read as follows:

“(i) the close of business on June 1, 2011,”

6. Section 7(a) is further amended by replacing the word “or” at the end of Section 7(a)(iii) with a comma and by adding the following clause immediately following the word “hereof” in Section 7(a)(iv):

“, or (v) the moment in time immediately prior to the Effective Time (as defined in Section 2.3 of the Merger Agreement) (the earlier to occur of the events described in clauses (i) and (v) of this section shall be referred to as the “Final Expiration Date”)”

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7. Section 11(a)(ii) of the Rights Agreement is hereby amended by adding the following sentence to the end of that section:

“Notwithstanding anything else set forth in this Agreement, no event requiring an adjustment under this Section 11(a)(ii) shall be deemed to have occurred by reason of (i) the execution and delivery or amendment of the Merger Agreement, (ii) the purchase by Purchaser of Common Stock pursuant to the Offer (and, if applicable, the Top-Up Option), (iii) the Merger, or (iv) the consummation of any other transaction contemplated by the Merger Agreement, as it may be amended from time to time.”

8. Sections 13(a)(x) and (y) of the Rights Agreement are amended to read as follows:

“(x) the Company shall consolidate with, or merge with and into, any other Person, (y) any Person shall consolidate with the Company, or merge with and into the Company and the Company shall be the continuing or surviving corporation of such merger (other than, in the case of either transaction described in (x) or (y), (i) a merger or consolidation which would result in all of the voting power represented by the securities of the Company outstanding immediately prior thereto continuing to represent (either by remaining outstanding or by being converted into securities of the surviving entity) all of the voting power represented by the securities of the Company or such surviving entity outstanding immediately after such merger or consolidation and the holders of such securities not having changed as a result of such merger or consolidation or (ii) the Merger),”

The remaining portion of Section 13(a) shall be unchanged and shall remain in full force and effect.

9. The first phrase of Section 13(c) of the Rights Agreement is hereby amended to read as follows:

“The Company shall not consummate any such consolidation (other than the Merger), merger (other than the Merger), sale or transfer unless the Principal Party shall have a sufficient number of authorized shares of its Common Stock that have not been issued or reserved for issuance to permit the exercise in full of the Rights in accordance with this Section 13 and unless prior thereto the Company and each Principal Party and each other Person who may become a Principal Party as a result of such consolidation, merger, sale or transfer shall have executed and delivered to the Rights Agent a supplemental agreement providing for the terms set forth in paragraphs (a) and (b) of this Section 13 and further providing that, as soon as practicable after the date of any consolidation, merger, sale or transfer of assets mentioned in paragraph (a) of this Section 13, the Principal Party at its own expense shall: . . .”

The remaining portion of Section 13(c) shall be unchanged and shall remain in full force and effect.

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10. Section 14(a)(i) of the Rights Agreement is hereby amended to read as follows:

“(i) consolidate with (other than the Merger),”

11. Section 14(a)(ii) of the Rights Agreement is hereby amended to read as follows:

“(ii) merge with or into (other than by the Merger),”

12. That certain Amendment No. 3 to Rights Agreement dated March 24, 2007 by and between the Company and the Rights Agent is hereby terminated and shall be of no further legal force or effect.

13. The Rights Agreement, as amended by this Amendment, shall remain in full force and effect in accordance with its terms.

14. All the covenants and provisions of this Amendment by or for the benefit of the Company or the Rights Agent shall bind and inure to the benefit of their respective successors and assigns hereunder.

15. Nothing in this Amendment shall be construed to give to any person or corporation other than the Company, Parent, Purchaser, the Rights Agent and the registered holders of the Rights Certificates (and, prior to the Distribution Date, the Common Stock) any legal or equitable right, remedy or claim under this Amendment; but this Amendment shall be for the sole and exclusive benefit of the Company, Parent, Purchaser, the Rights Agent and the registered holders of the Rights Certificates (and, prior to the Distribution Date, the Common Stock).

16. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

17. This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such state applicable to contracts to be made and performed entirely within such state.

18. This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

19. The Company hereby certifies to the Rights Agent that this Amendment is in compliance with Section 27 of the Rights Agreement.

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IN WITNESS WHEREOF, the parties herein have caused this Amendment to be duly executed and attested, all as of the date and year first above written.

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