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Given a task set T, finding a feasible schedule for T is one of the most significant problems of real time embedded systems. The research community has found a lot of important results for the scheduling problem on both uniprocessor and multiprocessor platforms. To the best of our knowledge, there is still room for research in determining the number of processors for a given task set, where each task is specified by its starting time, computation time, and deadline. The present paper describes an improved lower bound on the number of processors that allows a feasible schedule for a single-instance, non-preemptive, and independent task set T. In addition, an efficient algorithm is described, in order to achieve a feasible schedule for T for the real-time system with the number of processors equal to the lower bound previously determined. Both the above facts are extensions of the results presented in a previous work. Among many improvements, one of the main differences consists in considering the start times of the tasks when defining the task set, hence by allowing the considered model to cover more practical situations.