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A fast algorithm for the well-known Parzen window method to estimate density functions from the samples is described. The computational efforts required by the conventional and straightforward implementation of this estimation procedure limit its practical application to data of low dimensionality. The proposed algorithm makes the computation of the same density estimates with a substantial reduction of computer time possible, especially for data of high dimensionality. Some simulation experiments are presented which demonstrate the efficiency of the method. They indicate the computational savings that may be achieved through the use of this fast algorithm for artificially generated sets of data.