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Under some rank condition, a new version of bounded real lemma, which is expressed in terms of an admissible solution of a generalized discrete-time algebraic Riccati equation (GDARE) rather than inequality, is presented for linear discrete-time descriptor systems. When a linear discrete-time descriptor system is admissible, with the H∞-norm of its transfer matrix less than a prescribed positive number γ, a constructive procedure is also given to obtain an admissible solution of the above-mentioned GDARE.