Abdelzaher et al. proposed an algorithm to determine the schedulability of aperiodic tasks on multiprocessor systems, and proved that the aperiodic tasks are schedulable if the upperbound of synthetic utilization is less than or equal to 0.59. But this algorithm has a drawback in that if some tasks, even though they are completed and have no more execution times, are included in the current invocation set, their execution times and deadlines are added to the synthetic utilization. This may lead to a problem in which actually schedulable tasks are decided not to be schedulable. In this paper, we recognize the above mentioned problem and propose an improved synthetic utilization method that can be used to schedule aperiodic tasks more efficiently on multiprocessor systems.