Let OASRn×n = {J|JTJ = JJT = In, J = -JT, J ∈ Rn×n}.Given J ∈OASRn×n,A ∈ Cn×n is termed generalized Hamilton matrix ifJ AT = AH. we denote the set of all n × n generalized Hamilton matrics byHTCn×n, A ∈ Cn×n is termed generalized antihamilton matrix if JAJ = -AH.We denote the set of all n × n generalized antihamilton matrices by AHTCn×n.A ∈ Cn×n is termed Hermite-generalized antihamilton matrix ifAH=A and JAJ=-AH.We denote the set of all n × n Hermite-generalized antihamilton matrices byHAHCn×n.LetS = {A ∈ HAHCn×n|AZ = Y,ZHiYi = YHiHXi,YiZi+Zi = Yi, i = 1,2, Z, Y ∈ Cn×l}In this paper, we discuss the following two problems:Problem Ⅰ. Given X, B ∈ Cn×m, Find A ∈ S such thatf(A) ‖AX - B‖ = minProblem Ⅱ. Given A* ∈ Cn×n, Find ∈ SE such that‖A* - ‖ = infA∈SE ‖A* - A‖Where ‖@‖ is Frobenius norm, and SE is the solution set of Problem Ⅰ.The general representation of SE has been given. The necessary and sufficientconditions have been presented for f(A) = 0. For Problem Ⅱ the expression of thesolution has been provided.