The well known real time periodic task model first studied by C.L. Liu and J.W. Layland (1973) assumes that each task /spl tau/ has a worst case computation time C and each execution (instance) of the task takes no more than C time units. Based on the worst case computation time assumption, Liu and Layland derived a utilization bound under which all task sets are schedulable by the fixed priority scheduling scheme. The assumption and the derived utilization bound are, however too pessimistic when the average computation times of the tasks are smaller than their worst case computation times. To improve the schedulability test for such task sets, A.K. Mok and D. Chen (1996) proposed a multiframe task model for characterizing real time tasks whose computation times vary instance by instance. They also derived an improved utilization bound for multiframe task sets. Although Mok and Chen's utilization bound is better than Liu and Layland's bound, it is still too pessimistic in the sense that a lot of feasible task sets may not be found schedulable using their utilization bound. C.-C. Han and H. Yion Tyan (1997) proposed a new, better polynomial time schedulability test for periodic task model. They found that a similar technique can be applied to the multiframe task model. We discuss how the previously proposed schedulability test can be modified for a multiframe task model. We also show that our schedulability test is much better than using Mok and Chen's utilization bound by giving theoretical reasoning and presenting thorough performance evaluation results.