STOCK APPRECIATION RIGHT AGREEMENT UNDER STEREOTAXIS, INC. 2002 STOCK INCENTIVE PLAN (June, 2005)

Exhibit 10.4

STOCK APPRECIATION RIGHT AGREEMENT

UNDER

STEREOTAXIS, INC.

2002 STOCK INCENTIVE PLAN

(June, 2005)

THIS AGREEMENT, made effective as of [date], by and between Stereotaxis, Inc. (the “Company”), and                              (“Optionee”);

WITNESSETH THAT:

WHEREAS, the Board of Directors of the Company (the “Board of Directors”) has adopted the Stereotaxis, Inc. 2002 Stock Incentive Plan (the “Plan”) pursuant to which stock options, performance share awards, restricted stock and stock appreciation rights with respect to shares of the common stock of the Company may be granted to employees of the Company and its subsidiaries and certain other individuals; and

WHEREAS, the Company desires to grant to Optionee an award of              (            ) stock appreciation rights for the right to receive shares of the Company’s common stock (“Shares”) in payment of the increase in value of an equivalent number of Shares under the terms hereinafter set forth (“Stock Appreciation Right” or “SAR”);

NOW, THEREFORE, in consideration of the premises, and of the mutual agreements hereinafter set forth, it is covenanted and agreed as follows:

1. Award Subject to Plan. This SAR is granted under and is expressly subject to, all the terms and provisions of the Plan, which terms are incorporated herein by reference. The Optionee hereby acknowledges receipt of a copy of the Plan and agrees to be bound by all the terms and provisions thereof. Terms not defined herein shall have the meaning ascribed thereto in the Plan. The Committee referred to in Paragraph 4 of the Plan (“Committee”) has been appointed by the Board of Directors, and designated by it, as the Committee to make grants of SARs.

2. Grant and Terms of SARs. Pursuant to action of the Committee, which action was taken on [date] (“Date of Grant”), the Company grants to Optionee              Stock Appreciation Rights related to the increase in value of the equivalent number of Shares underlying this grant. The exercise price of these SARs is equal to $7.80 per SAR, which amount shall in no event be less than the fair market value of the underlying Shares on the Date of Grant (“Exercise Price”). Upon exercise of a SAR, the Optionee will receive, in Shares, the equivalent value equal to a) the closing price on the date of such exercise (“Exercise Date”) of a Share minus the Exercise Price, the net difference being multiplied by b) the number of SARs

being exercised on such Exercise Date. The number of Shares to be received shall be equal to the value so calculated divided by the closing price of the Shares on the Exercise Date. The term of this Agreement shall begin on the Date of Grant and end on the date that is five (5) years after the Date of Grant, and these SARs shall be exercisable for a period of five (5) years from the Date of Grant; provided, however, that the right to exercise such SARs shall be, and is hereby, restricted so that no SARs may be exercised prior to the first annual anniversary of the Date of Grant; that at any time during the term of this Agreement on or after the first annual anniversary of the Date of Grant, Optionee may exercise up to 25% of the total number of SARs to which this grant relates; that as of the first day of each calendar month after the first annual anniversary of the Date of Grant during the term of this Agreement, Optionee may exercise up to an additional 2.0833% of the total number of SARs to which this grant relates; so that on the fourth annual anniversary of the Date of Grant during the term hereof, Optionee will have become entitled to exercise the entire number of SARs to which this grant relates. Notwithstanding the foregoing, in the event of a Change of Control (as hereinafter defined) and if Optionee is involuntarily terminated for reasons other than Cause or terminates for Good Reason on or within one (1) year after the date of the Change of Control, Optionee may exercise 100% of the total number of SARs to which this grant relates. However, in no event may this grant or any part thereof be exercised after the expiration of five (5) years from the Date of Grant.

3. Definitions. For purposes of the Award, the following terms shall have the following meanings, except where otherwise noted:

(a) “Cause” shall mean Optionee’s fraud or willful misconduct as determined by the Committee

(b) “Change of Control” shall mean:

(i) The purchase or other acquisition (other than from the Company) by any person, entity or group of persons, within the meaning of Section 13(d) or 14(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”) (excluding, for this purpose, the Company or its subsidiaries or any employee benefit plan of the Company or its subsidiaries), of beneficial ownership (within the meaning of Rule 13d-3 promulgated under the Exchange Act) of 20% or more of either the then-outstanding shares of common stock of the Company or the combined voting power of the Company’s then-outstanding voting securities entitled to vote generally in the election of directors; or

(ii) Individuals who, as of the date hereof, constitute the Board of Directors of the Company (the “Board” and, as of the date hereof, the “Incumbent Board”) cease for any reason to constitute at least a majority of the Board, provided that any person who becomes a director subsequent to the date hereof whose election, or nomination for election by the Company’s shareholders, was approved by a vote of at least a majority of the directors then comprising the

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Incumbent Board (other than an individual whose initial assumption of office is in connection with an actual or threatened election contest relating to the election of directors of the Company, as such terms are used in Rule 14a-11 of Regulation 14A promulgated under the Exchange Act) shall be, for purposes of this section, considered as though such person were a member of the Incumbent Board; or

(iii) The consummation of a reorganization, merger or consolidation, in each case with respect to which persons who were the stockholders of the Company immediately prior to such reorganization, merger or consolidation do not, immediately thereafter, own more than 50% of, respectively, the common stock and the combined voting power entitled to vote generally in the election of directors of the reorganized, merged or consolidated corporation’s then-outstanding voting securities, or of a liquidation or dissolution of the Company or of the sale of all or substantially all of the assets of the Company.

(c) “Company” shall mean Stereotaxis, Inc., a Delaware corporation.

(d) “Company Stock” shall mean common stock of the Company.

(e) “Disability” or “Disabled” shall mean Optionee is permanently and totally disabled within the meaning of Section 422(c)(6) of the Internal Revenue Code of 1986, as amended, which, as of the date hereof, shall mean that Optionee is unable to engage in any substantial gainful activity by reason of any medically determinable physical or mental impairment which can be expected to result in death or which has lasted or can be expected to last for a continuous period of not less than 12 months. Optionee shall be considered Disabled only if Optionee furnishes such proof of Disability as the Committee may require.

(f) “Good Reason” shall mean”:

(i) Requiring Optionee to be based at any office or location more than 50 miles from Optionee’s office or location as of the date of the Change of Control;

(ii) The assignment to Optionee of any duties inconsistent in any respect with Optionee’s position (including status, offices, titles and reporting requirements), authority, duties or responsibilities as of the date of the Change of Control or any action by the Company or any of its subsidiaries which results in a diminution in such position, authority, duties or responsibilities, excluding for this purpose an action taken by the Company or one of its subsidiaries, to which Optionee objects in writing by notice to the Company within 10 business days after Optionee receives actual notice of such action, which is remedied by the Company or one of its subsidiaries promptly but in any event no later than 5 business days after Optionee provided such notice; or

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(iii) The reduction in Optionee’s total compensation and benefits below the level in effect as of the date of the Change of Control.

4. Anti-Dilution Provisions. In the event that, during the term of this Agreement, there is any change in the number or kind of shares of outstanding Common Stock of the Company by reason of stock dividends, recapitalizations, mergers, consolidations, split-ups, combinations or exchanges of shares and the like, the number of SARs and underlying Shares covered by this Agreement and the price thereof shall be adjusted, to the same proportionate number of SARs and underlying Shares and price as in this original Agreement.

5. Non-Transferability. Neither the SARs hereby granted nor any rights thereunder or under this Agreement may be assigned, transferred or in any manner encumbered except by will or the laws of descent and distribution, and any attempted assignment, transfer, mortgage, pledge or encumbrance except as herein authorized, shall be void and of no effect. The SARs may be exercised during Optionee’s lifetime only by Optionee. Notwithstanding the foregoing, the SARs may be transferred by gift or otherwise to a member of Optionee’s immediate family and/or trusts whose beneficiaries are members of Optionee’s immediate family, or to such other persons or entities as may be approved by the Committee.

6. Termination of Service. Optionee must exercise the SARs prior to Optionee’s termination of service, except that if the service of Optionee terminates without Cause (as hereinafter defined) Optionee may exercise the SARs, to the extent that Optionee was entitled to exercise them at the date of such termination of service, at any time within six (6) months after such termination, but not after five (5) years from the Date of Grant. For purposes of this paragraph only, “Cause” shall mean Optionee’s fraud or willful misconduct as determined by the Committee. If Optionee terminates service on account of Disability, Optionee may exercise such SARs to the extent Optionee was entitled to exercise them at the date of such termination, at any time within one (1) year of the termination of service, but not after five (5) years from the Date of Grant. The SARs hereby granted shall not be affected by any change of service so long as Optionee continues to be a service provider to the Company or a subsidiary thereof. Nothing herein shall confer on Optionee the right to continue in the service of the Company or any subsidiary or interfere in any way with the right of the Company or any subsidiary thereof to terminate Optionee’s service at any time.

7. Death of Optionee. In the event of the death of Optionee during the term of this Agreement and while Optionee is providing services to the Company (or a subsidiary), or within ninety (90) days after the termination of Optionee’s service (or one (l) year in the case of the termination of service if Optionee is disabled as determined above), this SAR may be exercised, to the extent that Optionee was entitled to exercise it at the date of death, by a legatee or legatees of Optionee under Optionee’s last will, or by Optionee’s personal representatives or distributees, at any time within a period of one (1) year after Optionee’s death, but not after five (5) years from the date hereof, and only if and to the extent that Optionee was entitled to exercise the SAR at the date of Optionee’s death.

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8. Shares Issued on Exercise of SARs. It is the intention of the Company that on any exercise of these SARs it will transfer to Optionee shares of its authorized but unissued stock or transfer Treasury shares, or utilize any combination of Treasury shares and authorized but unissued shares, to satisfy its obligations to deliver shares on any exercise hereof; provided that, the Company shall withhold sufficient shares to satisfy the Company’s obligation to withhold for tax requirements in respect of such payment if Optionee is is at the time of vesting subject to the Company’s policies regarding restrictions on trading within specified trading “windows”, and the Company may, in its sole discretion, so withhold if Optionee is not subject to such restrictions upon Optionee’s request. In the event that the Company withholds shares as contemplated in this Section, the Optionee shall receive a net number of shares equal to the shares to which the Optionee is otherwise entitled hereunder upon exercise, less the number of shares withheld by the Company hereunder. In the event that the Company determines not to withhold shares for an Optionee who is not subject to the trading restrictions prior to the payment on exercise, the Optionee must pay, or make arrangements acceptable to the Company for the payment of, any and all tax withholding that in the opinion of the Company is required by law. Such arrangements for payment of withholding may include, for example, directing an appropriate broker to sell such number of shares as necessary to result in a cash amount equal to the withholding requirements.

9. Committee Administration. These SARs have been granted pursuant to a determination made by the Committee, and such Committee or any successor or substitute committee authorized by the Board of Directors or the Board of Directors itself, subject to the express terms of these SARs, shall have plenary authority to interpret any provision of this grant and to make any determinations necessary or advisable for the administration of this grant and the exercise of the rights herein granted, and may waive or amend any provisions hereof in any manner not adversely affecting the rights granted to Optionee by the express terms hereof.

10. Choice of Law. This Agreement shall be governed by the laws of the State of Delaware, excluding any conflicts or choice of law rule or principle that might otherwise refer construction or interpretation of the Agreement to the substantive law of another jurisdiction. Optionee is deemed to submit to the exclusive jurisdiction and venue of the federal or state courts of Missouri, County of St. Louis, to resolve any and all issues that may arise out of or relate to this Agreement.

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Executed this      day of             , 20    .

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