AMENDMENT NO. ONE TO THE RIGHTS AGREEMENT

Exhibit 10.4

AMENDMENT NO. ONE

TO THE RIGHTS AGREEMENT

This Amendment No. One (this “Amendment”) to the Rights Agreement, dated as of November 2, 1999 (the “Agreement”), and effective this 21^st day of April 2005, is made and entered into by and between Matrix Service Company, a Delaware Corporation (the “Company”) and UMB Bank, N.A., as Rights Agent (the “Rights Agent”).

RECITALS

WHEREAS, on April 14, 2005, the Board of Directors of the Company (the “Board”) authorized the Securities Purchase Agreement (the “SPA”) among the Company and the investors named on the signature pages thereto (each individually, an “Investor”), and

WHEREAS, the Board has determined it to be in the best interests of the Company and its shareholders to amend the Agreement as herein provided in order to permit the transactions contemplated by the SPA.

NOW, THEREFORE, considering the premises and in consideration of the mutual agreements herein contained, the parties hereto hereby agree to amend the Agreement as follows:

1. The definition of “Acquiring Person” contained in Section 1 (a) of the Agreement is hereby amended as follows:

(a) The following shall be added following the second sentence of such definition:

“Notwithstanding the first sentence of this definition, no Investor shall be deemed to be or to have become an Acquiring Person solely as a result of the purchase of the Investor Securities on the Closing Date unless and until such time thereafter as such Investor shall increase its Beneficial Ownership of Common Shares to an amount in excess of such Investor’s then applicable Investor’s Percentage (as defined below); provided, however, that such Investor will not be deemed to be an Acquiring Person solely as a result of a reduction in the number of Common Shares outstanding unless and until such time after such reduction as (i) such Investor becomes the Beneficial Owner of additional Common Shares (other than as a result of a stock dividend, stock split or similar transaction effected by the Company in which all holders of Common Shares are treated equally) and after giving effect to such additional Common Shares such Investor is the Beneficial Owner of an amount in excess of such Investor’s then applicable Investor’s Percentage, or (ii) any other Person who is a Beneficial Owner of

Common Shares becomes an Affiliate or Associate of such Investor and after giving effect thereto such Investor is the Beneficial Owner of an amount in excess of such Investor’s then applicable Investor’s Percentage.”

(b) The fourth word in the last sentence of such definition is hereby changed from “three” to “four.”

2. The following definitions are hereby added to Section 1 of the Agreement in their proper alphabetical order and any cross-references to subsections of Section 1 are modified as appropriate:

“Closing Date” means the date of closing of the purchase and sale of the Investor Securities pursuant to the Securities Purchase Agreement.

“Investor” means each named as an “Investor” in the Securities Purchase Agreement that purchased Investor Securities on the Closing Date.

“Investor’s Percentage” means, as to each Investor (a) as of the Closing Date, the ratio (expressed as a percentage) that the number of Common Shares issuable upon conversion of the Investor Securities purchased by such Investor on the Closing Date bears to the total number of Common Shares outstanding on the Closing Date (including as outstanding the total number of Common Shares issuable upon conversion of all Investor Securities purchased by all Investors on the Closing Date); and (b) at any time after such Investor becomes the Beneficial Owner of less than 15% of the outstanding Common Shares, 15% or more of the then outstanding Common Shares, then the immediately preceding sentence shall be deemed to be deleted from this Agreement and the Investors shall be subject to the first sentence of this Section 1(a).

“Investor Securities” means the securities purchased by Investors on the Closing Date pursuant to the Securities Purchase Agreement.

“Securities Purchase Agreement” means the agreement so captioned and dated April 21, 2005, by and between the Company and each Investor, pursuant to which the Company issued and sold the Investor Securities to the Investors.

3. Except as expressly modified herein, the Agreement shall remain in full force and effect.

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4. This Amendment may be executed in one or more counterparts, each of which shall be deemed an original and all of which shall constitute one and the same instrument. The delivery of this Amendment by facsimile shall be effective for all purposes.

IN WITNESS WHEREOF, each party hereto has caused this Amendment to be duly executed on its behalf as of the date first set forth above.

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