Based on sufficiently studying properties of bisymmetric matrices

solving the bisymmetric solutions of the matrix equation AX=B is equivalently reformulated into the problem for solving symmetric solutions of a class of matrix equations.By means of common solutions of the simple latter problem

bisymmetric solutions of the matrix equation AX=B are easily obtained and the expression of the solution set is also given.Moreover

the optimal approximation problem of the bisymmetric solution set of the matrix equation AX=B is also studied.When the matrix equation AX=B has an bisymmetric solution

its optimal approximation solution exists uniquely.The expression of the optimal approximation solution is provided.