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This work addresses the development of a hybrid CPU-GPU local search heuristic for the unrelated parallel machine scheduling problem. In this scheduling problem setup times are sequence-dependent and also machine-dependent. The objective is to minimize the maximum completion time of the schedule, known as make span. Since the problem belongs to the NP-hard class there is no known polynomial time algorithm to solve it, so metaheuristics and local search heuristics are usually developed to find good near optimal solutions. In general, the local search is the most expensive part of the heuristic method, so our algorithm harnesses the tremendous computing power of the GPU to decrease the local search computational time. We use the local search based on swapping jobs in different machines, since it is able find good near optimal solutions as we report from previous results in literature. We show that the hybrid CPU-GPU local search achieves average speedups from 10 to 27 times in relation to the pure CPU local search.