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Scheduling of tasks in a heterogeneous computing (HC) environment is a critical task. It is also a well-known NP-complete problem, and hence several researchers have presented a number of heuristics for the same. The paper begins with introducing a new heuristic called Sympathy, and later a variant called Segmented Sympathy. A new Genetic Algorithm based heuristic using the Segmented Sympathy heuristic is proposed, which is aimed at improving over the speed and makespan of the implementation by Braun et al. Finally, the results of Simulation reveal that the proposed Genetic Algorithm gave up to 8.34% and on an average 3.42% better makespans. The new heuristic is also about 160% faster with respect to the execution time.