This paper is concerned with the determination of suboptimal feedback laws for the linear systems with quadratic performance criteria. The time-varying gains are approximated by the piecewise constant gains which are naturally determined by using Walsh functions. An increase of the number of intervals of Walsh functions enables us to approximate the true optimal control more closely ; and a decrease of the number of intervals makes the implementation easier. Therefore the proposed method is simple in theory and flexible in practice. The beginning part of the paper, being tutorial in nature, is on Walsh functions, the middle part developes an operational method for solving state equations and the final part is concentrated on the Walsh functions approach to the solution of piecewise constant gains of optimal control.