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A method for the design of a robust model matching controller for nonminimum phase discrete-time systems in the presence of unmodeled dynamics is proposed. This controller robustly stabilizes the nominal plant in the presence of unmodeled dynamics and achieves the desired model matching simultaneously. Furthermore, in this method, we introduce the output loop compensator for the unmodeled dynamics. Sufficient condition for stabilizing the nominal plant in the presence of unmodeled dynamics has been established. Finally, the results of computer simulation are presented to illustrate the effectiveness of the proposed method.