In order to tolerate faults which may occur during the execution of distributed tasks in high-performance parallel computer systems, tasks are duplicated on different processors. In this paper, by utilizing the task duplication based scheduling algorithm, a new task scheduling algorithm which duplicates each task on more than two different processors with the minimum schedule length is presented, and the number of processors required for the duplication is analyzed with the ratio of communication cost to computation time and the workload of the system. A simulation with various task graphs reveals that the number of processors required for the full-duplex fault-tolerant task scheduling with the obtainable minimum schedule length increases about 30% to 75% when compared with that of the task duplication based scheduling algorithm.