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This paper is mainly conceed with solving the following two problems:Problem Ⅰ.Given X ∈Cn×m,(A)=diag(λ1，λ2…,λm)∈Cm×m.Find A∈ABSRn×n such thatAX = XAwhere ABSRn×n is the set of all real n × n anti-bisymmetric matrices.Problem Ⅱ. Given A* ∈ Rn×n. Find (A^) ∈ SE such that‖A*-(A^)‖F=min A∈SE‖A*-A‖F,where ‖ @ ‖F is Frobenius norm, and SE denotes the solution set of Problem I.The necessary and sufficient conditions for the solvability of Problem Ⅰ have been stud-ied. The general form of SE has been given. For Problem Ⅱ the expression of the solutionhas been provided.