A multiprocessor scheduling algorithm named U-EDF, was presented in [1] for the scheduling of periodic tasks with implicit deadlines. It was claimed that U-EDF is optimal for periodic tasks (i.e., it can meet all deadlines of every schedulable task set) and extensive simulations showed a drastic improvement in the number of task preemptions and migrations in comparison to state-of-the-art optimal algorithms. However, there was no proof of its optimality and U-EDF was not designed to schedule sporadic tasks. In this work, we propose a generalization of U-EDF for the scheduling of sporadic tasks with implicit deadlines, and we prove its optimality. Contrarily to all other existing optimal multiprocessor scheduling algorithms for sporadic tasks, U-EDF is not based on the fairness property. Instead, it extends the main principles of EDF so that it achieves optimality while benefiting from a substantial reduction in the number of preemptions and migrations.