Abstract: First, an unsymmetric tridiagonal matrixTis transformed into a symmetric tridiagonal matrix T*. Then, with the symmetric tridiagonal matrixT*and a displacementσgiven, an algorithm of solving for the simplified matrixT^from the matrixT*is presented. Thus, the eigenvalues of the symmetric tridiagonal matrix are obtained byQRmethod with Wilkinson displacement. The concrete algorithm is easy to implement on computers.