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Optimal scheduling of parallel tasks with some precedence relationship, onto a parallel machine is known to be NP-complete. The complexity of the problem increases when task scheduling is to be done in a heterogeneous environment, where the processors in the network may not be identical and take different amounts of time to execute the same task. We introduce a task duplication-based scheduling algorithm for network of heterogeneous systems (TANH), with complexity O(V2), which provides optimal results for applications represented by directed acyclic graphs (DAGs), provided a simple set of conditions on task computation and network communication time could be satisfied. The performance of the algorithm is illustrated by comparing the scheduling time with an existing "best imaginary level scheduling (BIL)" scheme for heterogeneous systems. The scalability for a higher or lower number of processors, as per their availability is also discussed. We have shown to provide substantial improvement over existing work on the task duplication-based scheduling algorithm (TDS).