This paper deals with the design of optimal discrete control systems with prescribed eigenvalues. Solheim's method for such design is improved and extended to achieve the original design objective. That is the minimization of a quadratic performance index with a prescribed control weighting matrixRand some state weighting matrixQ. A new recursive algorithm is also presented. While this algorithm retains the simplicity provided by Solheim's method, it constructs the resultant state weighting matrix Q as the sum of the recursive state weighting matrices <?(. The algorithm is general and applicable to any system structure. For the sake of completeness, the optimality of Solheim's solution is tested by using a simple necessary condition which is developed in the paper. It is shown that the optimality of Solheim's solution is not. in general, guaranteed.