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We propose a multistage pattern recognition algorithm with a reject option. On every stage, the presented algorithm chooses a class of signal or rejects the signal, i.e. refuses to make a decision. If a class is assigned to the signal on some stage, then the algorithm stops. In the opposite case of a signal rejection, the decision of assigning to a class is made on the next stage. The multiresolution signal representation in wavelet bases allows to take a more accurate signal representation on every following stage. Our approach saves the computation time, when the algorithm selects a class on an early stage basing on a coarse wavelet representation. If the inaccurate representation is insufficient to point out one of classes (e.g. when the a posteriori probability of every class is lower than a fixed bound, in case of Bayesian classifier), the reject option protects from choosing a wrong class. We show that a risk of misclassification for the Bayesian decision rule with a reject option is lower or equal to a risk of the one-stage optimal Bayesian rule.