Real-time systems using rate-monotonic fixed priority scheduling can be checked for schedulability either by sufficient but pessimistic schedulability conditions or by exact testing. Exact testing provides a more precise result but may not be performed in polynomial time. Audsley et al. proposed one of the earliest methods by iteratively deriving the response times of jobs. Other researchers have improved the exact test method by using different initial values for testing. In this paper, we propose new initial values of p, - p, , and f in a task set of i tasks, where p, is the period of task Tl. We show that the new initial values can significantly improve the efficiency of exact testing. These period-dependent initial values can also be used for the schedulability test of multiframe task models and effectively reduce the number of iterations for testing.