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The real-time multiframe task model first studied by Mok and Chen assumes that the computation times of a periodic task vary instance by instance. They have derived an utilization bound for verifying the schedulability of multiframe task sets. Their schedulability test has since been improved by other researchers. In this paper we use the information about the relative period ratios between tasks in a system to derive a new schedulability condition. By considering the smallest and the largest period values in a system, we can show that the RM schedulability bound can be improved significantly. This method also can be applied to other test methods studied earlier to improve the schedulability of real-time multiframe systems.