An efficient computer algorithm to have assigned closed loop eigenvalues for designing optimal controllers of linear systems, based on the eigenvector of the matrix Riccati equation via-reduced order model is presented. All the known methods of the above problem are based on shifting the complex eigenvalues one after the other. An attempt has been made to shift the two complex eigenvalues in a single at- tempt. The algorithm is designed in such a way that complex arithmetic is avoided. This not only saves the computer double storage but also CPU time.