For an n ${ imes}$ n real matrix X, let ${Phi}$(X) = X o (X$^$-1/)$^$T/, where o stands for the Hadamard (entrywise) product. Suppose A, B, G and D are n ${ imes}$ n real nonsingular matrices, and among them there are at least one solutions to the equation (equation omitted). An equivalent condition which enable (equation omitted) become a real solution ot the equation (equation omitted), is given. As application, we get new real solutions to the matrix equation (equation omitted) by applying the results of Zhang. Yang and Cao [SIAM.J.Matrix Anal.Appl, 21(1999), pp: 642-645] and Chen [SIAM.J.Matrix Anal.Appl, 22(2001), pp:965-970]. At the same time, all solutions of the matrix equation (equation omitted) are also given.