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The heterogeneous distributed computing system consists of network of heterogeneous computers and the applications to execute on it. The applications may have different deadline criteria. Based on the nature of the deadline, the applications are categorised as mission-critical, firm and soft. In this paper, a load balanced algorithm is proposed for non-pre-emptively scheduling a bag of independent tasks in a heterogeneous computing environment. The load of a machine is the sum of execution times of tasks that are currently scheduled in it. This scheduler has three major goals i)To maximize the number of mission-critical tasks meeting their deadline ii)To maximize the total number of tasks meeting their deadline iii) To achieve a load balance on all the machines by minimising the load difference. The algorithm is compared for various performance metrics, with the other algorithms in the literature and proves to be better.