The matrix least squares (LS) problem minx ‖AXB~T-T‖_F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem min_(x_1,x_2)‖A_1X_1B_1~T+A_2X_2B_2~T-T‖_F can also be regarded as the constrained LS problem min_x=diag(x_1,x_2) ‖AXB~T-T‖F with A=[A_1, A_2] and B=[B_1, B_2]. The authors transform T to (T) such that min_(x_1,x_2)‖A_1X_1B_1~T+A_2X_2B_2~T-T‖F is equivalent to min_x=diag(x_1,x_2)‖AXB~T-(T)‖_F whose solutions are included in the solution set of unconstrained problem minx ‖AXB~T-(T)‖_F. So the general solutions of min_(x_1,x_2)‖A_1X_1B_1~T+A_2X_2B_2~T-T‖_F are reconstructed by selecting the parameter matrix in that of minx ‖AXB~T-(T)‖_F.