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We propose a fast algorithm for speeding up the process of template matching that uses M-estimators for dealing with outliers. We propose a particular image hierarchy called the p-pyramid that can be exploited to generate a list of ascending lower bounds of the minimal matching errors when a nondecreasing robust error measure is adopted. Then, the set of lower bounds can be used to prune the search of the p-pyramid, and a fast algorithm is thereby developed in this paper. This fast algorithm ensures finding the global minimum of the robust template matching problem in which a nondecreasing M-estimator serves as an error measure. Experimental results demonstrate the effectiveness of our method.