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Marzal and Vidal [8] recently considered the problem of computing the normalized edit distance between two strings, and reported experimental results which demonstrated the use of the measure to recognize hand-written characters. Their paper formulated the theoretical properties of the measure and developed two algorithms to compute it. In this short communication we shall demonstrate how this measure is related to an auxiliary measure already defined in the literature驴the inter-string constrained edit distance[10], [11], [15]. Since the normalized edit distance can be computed efficiently using the latter, the analytic and experimental results reported in [8] can be obtained just as accurately, but more efficiently, using the strategies presented here.