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Many pattern recognition computer programs use one of the clustering algorithm techniques. Often these algorithms use a Euclidean distance metric as a similarity measure. A scheme is proposed where both the Euclidean metric and a more simple city-block metric are utilized together to reduce overall classification time. The relation between the Euclidean and city-block distances is introduced as a scalar function. The bounds of the function are given and used to decide whether classification of each pattern vector is to be achieved by the computationally slow Euclidean distance or the faster city-block distance. The criteria is that the classification should be identical to the original Euclidean only scheme.