Davis Wright Tremaine will move into Madison Centre, which is the sixth-biggest project under construction downtown.

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One of the region’s biggest law firms will take over eight floors of one of the largest high-rises under construction in downtown Seattle.

Davis Wright Tremaine will lease 22 percent of the 37-story Madison Centre, which is set to open in mid-2017, developers Schnitzer West and Cornerstone Real Estate Advisers announced Wednesday.

It’s the first tenant confirmed for the $157 million project at 5th Avenue and Madison Street, which developers had originally hoped to pre-lease before construction began in 2014, and is perhaps notable in that the tenant will not be a tech company.

The law firm, which has 550 attorneys around the country and in China, will relocate from its headquarters at 1201 Third Ave.

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Madison Centre is the sixth-most-expensive of about 65 projects under construction downtown, and the fourth biggest project containing office space behind two Amazon developments and The Mark hotel and office project.