In this paper, model reduction of discrete time linear systems is revisited. The main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem. The quality of the proposed suboptimal solution is assessed through comparisons, performed via simulation, with the already classical balanced truncation method. The results lead to the conclusion that the proposed method performs equivalently when the H-2 norm of the reduction error is considered and significantly better when the H-infinity norm is considered instead.