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In this paper, we explore the problem of scheduling parallel programs using task duplication for message-passing multicomputers. Task duplication means scheduling a parallel program by redundantly executing some of the tasks on which other tasks of the program critically depend. This can reduce the start times of tasks waiting for messages from tasks residing in other processors. There have been a few scheduling algorithms using task duplication. We discuss two such previously reported algorithms and describe their differences, limitations and suitability for different environments. A new algorithm is proposed which outperforms both of these algorithms, and is more efficient for low as well as high values of communication-to-computation ratios. The algorithm takes into account arbitrary computation and communication costs. All three algorithms are tested by scheduling some of the commonly encountered graph structures.