This paper studies the problem of H-infinity control of discrete-time singularly perturbed systems. A new sufficient condition, which ensures the existence of state feedback controllers such that the resulting closed-loop system is asymptotically stable while satisfying a prescribed H-infinity norm bound, is obtained. This condition is in terms of a linear matrix inequality, which is independent of the singular perturbation parameter. Furthermore, a new condition on searching for the allowable upper bound of the singular perturbation parameter is proposed, under which the discrete-time singularly perturbed system is asymptotically stable with an H-infinity norm bound when the singular perturbation parameter is lower than this upper bound. In these derived conditions, the upper bound of the singular perturbation parameter is not required to be smaller than one. The reduced conservatism of our results is demonstrated via a numerical example. (C) 2009 Elsevier Ltd. All rights reserved.