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A real n × n symmetric matrix X = (xij)n×n is called a bisymmetric matrix if xij = xn+1-j,n+1-i. Based on the projection theorem, the canonical correlation decomposition and the generalized singular value decomposition, a method useful for finding the least-squares solutions of the matrix equation ATXA = B over bisymmetric matrices is proposed. The expression of the least-squares solutions is given. Moreover, in the corresponding solution set, the optimal approximate solution to a given matrix is also derived. A numerical algorithm for finding the optimal approximate solution is also described.