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Tim Tebow‘s not second-string to Nike — because the athletic company is now suingReebok … over the exclusive rights to use Tebow’s name on merchandise.

Nike filed a lawsuit against Reebok this week — just one day after the Jets officially announced the Tebow trade — and according to the suit, Reebok’s new Jets merch bearing Tebow’s name (above) is in violation of a 2010 Nike-Tebow endorsement deal.

According to the deal, Nike’s got sole merchandising rights to all things Tebow … and Nike alone.

A rep for Nike released a statement, claiming, “We have filed a complaint relating to unauthorized use of Tim Tebow’s name on New York Jets related apparel. Nike is authorized and licensed to use Tim Tebow’s name on products.”

As for the 2010 endorsement deal — Nike made off like a bandit, signing Tebow before his jersey became one of the most sought-after in the league … for $300,000 a year.