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One common approach for partitioned multiprocessor scheduling problem is to transform this problem into a traditional bin-packing problem, with the utilization of a task being the "size" of the object and the utilization bound of a processor being the "capacity" of the bin. However, this approach ignores the fact that some implicit relations among tasks may significantly affect the feasibility of the tasks allocated to a processor. In this paper, we present a novel multiprocessor partitioned scheduling algorithm for fixed-priority sporadic real-time tasks based on the Rate Monotonic Scheduling (RMS) policy. Our approach takes advantage of the fact that harmonic tasks can achieve a much higher processor utilization than that defined by a utilization bound. As demonstrated in our experiment results, when taking the task period relationship into consideration, our algorithm can achieve a significant improvement over previous work.