TENDER AND STOCKHOLDER SUPPORT AGREEMENT

EXHIBIT 10.1

TENDER AND STOCKHOLDER SUPPORT AGREEMENT

This TENDER AND STOCKHOLDER SUPPORT AGREEMENT (this “Agreement”), dated March 24, 2007, is by and among: Beckman Coulter, Inc., a Delaware corporation (“Parent”); Louisiana Acquisition Sub, Inc., a Delaware corporation and a wholly owned subsidiary of Parent (“Purchaser”); and Kim D. Blickenstaff and Rita Blickenstaff (the “Stockholder”), a stockholder of Biosite Incorporated, a Delaware corporation (the “Company”).

WHEREAS, Parent, Purchaser and the Company propose to enter into an Agreement and Plan of Merger, dated as of the date hereof (the “Merger Agreement”), which provides, among other things, for Purchaser to conduct a tender offer for all of the issued and outstanding Company Shares (as defined below) of the Company (the “Offer”) and the merger of Purchaser with and into the Company, with the Company continuing as the surviving corporation (the “Merger”), upon the terms and subject to the conditions set forth in the Merger Agreement (capitalized terms used herein without definition shall have the respective meanings specified in the Merger Agreement);

WHEREAS, the Stockholder owns 241,946 issued and outstanding shares of common stock, par value $0.001 per share, of the Company (the “Company Shares”) (such Company Shares, together with any other issued and outstanding shares of capital stock of the Company acquired by the Stockholder after the date hereof and prior to the earlier of the Effective Time and the termination of all of the Stockholder’s obligations under this Agreement, including any Company Shares acquired by means of purchase, dividend or distribution, or issued upon the exercise of any warrants or options, or the conversion of any convertible securities or otherwise, being collectively referred to herein as the “Shares”); and

WHEREAS, as a condition to the willingness of Parent and Purchaser to enter into the Merger Agreement and as an inducement and in consideration therefor, the Stockholder has agreed to enter into this Agreement.

NOW, THEREFORE, in consideration of the foregoing and the mutual covenants and agreements set forth herein and in the Merger Agreement, and intending to be legally bound hereby, the parties hereto agree as follows:

SECTION 1. Representations and Warranties of the Stockholder. The Stockholder hereby represents and warrants to Parent and Purchaser as follows:

(a) The Stockholder (i) is the record or beneficial owner, and has good and marketable title to, the Shares, free and clear of any and all liens, claims, security interests, proxies, voting trusts or agreements, options, rights, understandings or arrangements or any other encumbrances whatsoever on title, transfer, or exercise of any rights of a stockholder in respect of such Shares (collectively, “Encumbrances”); (ii) does not own, of record or beneficially, any shares of capital stock of the Company (or rights to acquire any such shares) other than the Shares and other than Company Options to purchase up to 437,811 Company Shares); and (iii) has the sole right to vote, sole power

of disposition, sole power to issue instructions with respect to the matters set forth in Sections 3, 4, and 6 hereof, sole power of conversion, sole power to demand appraisal rights and sole power to agree to all of the matters set forth in this Agreement, in each case with respect to all of the Stockholder’s Shares, with no material limitations qualification or restrictions on such rights, subject to applicable federal securities law and the terms of this Agreement.

(b) The Stockholder has the legal capacity and all requisite power and authority to execute and deliver this Agreement and to perform the Stockholder’s obligations hereunder and consummate the transactions contemplated hereby. This Agreement has been duly and validly executed and delivered by the Stockholder, and constitutes a valid and binding obligation of the Stockholder enforceable in accordance with its terms, subject to the effects of bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally and general equitable principles (whether considered in a proceeding in equity or at law).

(c) The execution and delivery of this Agreement and the consummation by the Stockholder of the transactions contemplated hereby will not (i) result in a violation of, or a default under, or conflict with any contract, trust, commitment, agreement, understanding, arrangement or restriction of any kind to which the Stockholder is a party or by which the Stockholder or the Stockholder’s assets are bound, or (ii) violate, or require any consent, approval, or notice under, any provision of any judgment, order, decree, statute, law, rule or regulation applicable to the Stockholder.

SECTION 2. Representations and Warranties of Parent and Purchaser. Each of Parent and Purchaser hereby, jointly and severally, represents and warrants to the Stockholder as follows:

(a) Each of Parent and Purchaser is a corporation duly organized, validly existing and in good standing (with respect to jurisdictions which recognize such concept) under the laws of the jurisdiction in which it is incorporated, and each of Parent and Purchaser has all requisite corporate power and corporate authority to execute and deliver this Agreement and to perform its obligations hereunder and consummate the transactions contemplated hereby, and has taken all necessary corporate action to authorize the execution, delivery and performance of this Agreement.

(b) This Agreement has been duly authorized, executed and delivered by each of Parent and Purchaser, and constitutes a valid and binding obligation of Parent and Purchaser enforceable in accordance with its terms, subject to the effects of bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally and general equitable principles (whether considered in a proceeding in equity or at law).

(c) The execution and delivery of this Agreement and the consummation by Parent and Purchaser of the transactions contemplated hereby will not (i) result in a violation of, or a default under, or conflict with (x) any provisions of the

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organizational documents of Parent or Purchaser or (y) any contract, trust, commitment, agreement, understanding, arrangement or restriction of any kind to which such Parent or Purchaser is a party or by which Parent or Purchaser or their assets are bound, or (ii) violate, or require any consent, approval, or notice under, any provision of any judgment, order, decree, statute, law, rule or regulation applicable to Parent or Purchaser.

SECTION 3. Tender of the Shares.

(a) Unless this Agreement shall have been terminated in accordance with its terms, and subject to Section 4, the Stockholder hereby agrees that he shall (i) tender (and deliver any certificates evidencing) his Shares, or cause his Shares to be tendered, into the Offer promptly following the commencement of the Offer, and in any event no later than the third business day prior to the Initial Expiration Date, free and clear of all Encumbrances and (ii) not withdraw his Shares, or cause his Shares to be withdrawn, from the Offer at any time. Unless this Agreement shall have been terminated in accordance with its terms, and subject to Section 4, if the Stockholder acquires Shares after the date hereof, the Stockholder shall (i) tender or cause to be tendered such Shares on or before the third business day prior to the Initial Expiration Date or, if later, on or before the second business day after such acquisition but in any event prior to the date of expiration of the Offer and (ii) not withdraw his Shares, or cause his Shares to be withdrawn, from the Offer at any time.

(b) If the Offer is terminated or withdrawn by Purchaser, or the Merger Agreement is terminated prior to the purchase of Shares in the Offer, Parent and Purchaser shall promptly return, and shall cause any depository acting on behalf of Parent and Purchaser to return all tendered Shares to the registered holders of the Shares tendered in the Offer.

SECTION 4. Transfer of the Shares; Other Actions.

(a) Prior to the termination of this Agreement, except as otherwise provided herein (including pursuant to Section 3 hereof), without prior written consent of Parent or Purchaser, the Stockholder shall not: (a) transfer, assign, sell, gift-over, pledge or otherwise dispose (whether by sale, merger, consolidation, liquidation, dissolution, dividend, distribution or otherwise) of, or consent to any of the foregoing (“Transfer”), any or all of the Shares or any right or interest therein; (b) enter into any contract, option or other agreement, arrangement or understanding with respect to any Transfer; (c) grant any proxy, power-of-attorney or other authorization or consent with respect to any of the Shares; (d) deposit any of the Shares into a voting trust, or enter into a voting agreement or arrangement with respect to any of the Shares; or (e) take any other action that would in any way restrict, limit or interfere with the performance of the Stockholder’s obligations hereunder or the transactions contemplated hereby.

SECTION 5. Certain Events. In the event of any stock split, stock dividend, merger, reorganization, recapitalization or other change in the capital structure of the Company affecting the Company Shares or the acquisition of additional Company Shares or other securities or rights of the Company by the Stockholder, the number of Shares shall be adjusted appropriately, and this Agreement and the rights and obligations hereunder shall attach to any additional Company Shares or other securities or rights of the Company issued to or acquired by the Stockholder.

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SECTION 6. Covenant to Vote. Unless this Agreement shall have been terminated in accordance with its terms, the Stockholder hereby agrees to vote all Shares beneficially owned or controlled by the Stockholder (the “Vote Shares”), or to grant a consent or approval in respect of the Vote Shares, in connection with any meeting of the shareholders of the Company or any action by written consent in lieu of a meeting of shareholders of the Company (i) in favor of the Merger or any other transaction pursuant to which Parent proposes to acquire the Company, whether by tender offer, merger, or otherwise, in which stockholders of the Company would receive consideration per share of Company Shares equal to or greater than the consideration to be received by such stockholders in the Offer and the Merger, and/or (ii) against any action or agreement which would impede, interfere with or prevent the Merger, including, but not limited to, any other extraordinary corporate transaction, including, a merger, acquisition, sale, consolidation, reorganization or liquidation involving the Company and a third party, or any other proposal of a third party to acquire the Company or all or substantially all of the assets thereof.

SECTION 7. Further Assurances. The Stockholder shall, upon request of Parent or Purchaser, execute and deliver any additional documents and take such further actions as may reasonably be deemed by Parent or Purchaser to be necessary or desirable to carry out the provisions of this Agreement.

SECTION 8. Termination. This Agreement, and all rights and obligations of the parties hereunder, shall terminate on the earlier of: (a) the date the Merger Agreement is terminated in accordance with its terms; and (b) the Effective Time; provided, however, that (i) nothing herein shall relieve any party from liability for any breach hereof; and (ii) Section 10 and Section 11 shall survive any termination of this Agreement.

SECTION 9. Waiver of Appraisal and Dissenter’s Rights. The Stockholder waives and agrees not to exercise any rights of appraisal or rights to dissent from the Merger that the Stockholder may have with respect to the Stockholder’s Shares.

SECTION 10. Expenses. All fees, costs and expenses incurred in connection with this Agreement and the transactions contemplated hereby shall be paid by the party incurring such fees, costs and expenses.

SECTION 11. Miscellaneous.

(a) Notices. All notices and other communications hereunder shall be in writing and shall be deemed given if delivered personally, telecopied (which is confirmed) or sent by a nationally recognized overnight courier service, such as Fedex (providing proof of delivery), to the parties at the following addresses (or at such other address for a party as shall be specified by like notice):

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If to the Stockholder:

Kim D. Blickenstaff

Biosite Incorporated

9975 Summers Ridge Road

San Diego, CA 92121

Facsimile:    (858)  ###-###-####

with a copy to:

Biosite Incorporated

9975 Summers Ridge Road

San Diego, CA 92121

Attention:    David B. Berger, Vice President, Legal Affairs

Facsimile:   (858)  ###-###-####

and a copy to:

Cooley Godward Kronish LLP

4401 Eastgate Mall

San Diego, CA

92121-1909

Attention:    Fred Muto, Esq.

Facsimile:   (858)  ###-###-####

If to Parent or Purchaser, to:

Beckman Coulter, Inc.

4300 N. Harbor Boulevard

P.O. Box 3100

Fullerton, CA ###-###-#### USA

Attention:    General Counsel

Facsimile:   (714)  ###-###-####

with a copy to:

Latham & Watkins LLP

633 West Fifth St., Suite 4000

Los Angeles, CA 90071-2007

Attention:    Paul D. Tosetti, Esq.

                     Cary K. Hyden, Esq.

                     Jonn R. Beeson, Esq.

Facsimile:   (213)  ###-###-####

(b) Headings. The headings contained in this Agreement are for reference purposes only and shall not affect in any way the meaning or interpretation of this Agreement.

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(c) Counterparts. This Agreement may be executed manually or by facsimile by the parties hereto in any number of counterparts, each of which shall be considered one and the same agreement and shall become effective when a counterpart hereof shall have been signed by each of the parties and delivered to the other parties.

(d) Entire Agreement. This Agreement (together with the Merger Agreement and any other documents and instruments referred to herein and therein) constitutes the entire agreement among the parties with respect to the subject matter hereof and thereof and supersedes all other prior agreements and understandings, both written and oral, among the parties or any of them with respect to the subject matter hereof and thereof. This Agreement is not intended and does not confer upon any Person other than the parties hereto any rights hereunder.

(e) Governing Law. This Agreement shall be governed by and construed in accordance with the laws of the State of Delaware, without giving effect to the principles of conflicts of law thereof.

(f) Assignment. Neither this Agreement nor any of the rights, interests or obligations hereunder shall be assigned by any of the parties hereto (whether by operation of law or otherwise) without the prior written consent of the other parties except that Parent and Purchaser may assign, in their sole discretion and without the consent of any other party, any or all of their rights, interests and obligations hereunder to each other or to one or more direct or indirect wholly-owned subsidiaries of Parent (each, an “Assignee”). Any such Assignee may thereafter assign, in its sole discretion and without the consent of any other party, any or all of its rights, interests and obligations hereunder to one or more additional Assignees. Subject to the preceding sentence, this Agreement will be binding upon, inure to the benefit of and be enforceable by, the parties and their respective successors and assigns, and the provisions of this Agreement are not intended to confer upon any person other than the parties hereto any rights or remedies hereunder.

(g) Severability of Provisions. If any term or provision of this Agreement is invalid, illegal or incapable of being enforced by rule of law or public policy, all other conditions and provisions of this Agreement shall nevertheless remain in full force and effect so long as the economic or legal substance of the transactions contemplated by this Agreement is not affected in any manner adverse to any party. Upon such determination that any term or other provision is invalid, illegal or incapable of being enforced, the parties hereto shall negotiate in good faith to modify this Agreement so as to effect the original intent of the parties as closely as possible in an acceptable manner to the end that the transactions are fulfilled to the extent possible.

(h) Specific Performance. The parties hereto acknowledge that money damages would be an inadequate remedy for any breach of this Agreement by any party hereto, and that the obligations of the parties hereto shall be enforceable by any party hereto through injunctive or other equitable relief.

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(i) Amendment. No amendment, modification or waiver in respect of this Agreement shall be effective against any party unless it shall be in writing and signed by such party.

(j) Binding Nature. This Agreement is binding upon and is solely for the benefit of the parties hereto and their respective successors, legal representatives and assigns.

[signature page follows]

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IN WITNESS WHEREOF, Parent, Purchaser and the Stockholder have caused this Agreement to be duly executed and delivered as of the date first written above.

SIGNATURE PAGE TO TENDER AND STOCKHOLDER SUPPORT AGREEMENT