This paper concerns the bounded real lemma for discrete-time descriptor systems. A new formulation of the bounded real lemma for these systems is given. It extends the recent results presented in Zhang, Xia, and Shi (2008) and gives necessary and sufficient conditions in strict LMI (linear matrix inequality) which is more suitable for the control design than those presented in Zhang, Xia, and Shi (2008). An application to the H-infinity control design is given. A numerical example is presented to show the applicability of our approach. (C) 2011 Elsevier Ltd. All rights reserved.