For a system with multiple real-time tasks of different deadlines, it is very difficult to find the optimal checkpoint interval because of the complexity in considering the scheduling of tasks. In this paper, we determine the optimal checkpoint interval for multiple real-time tasks that are scheduled by RM(Rate Monotonic) algorithm. Faults are assumed to occur with Poisson distribution. Checkpoints are inserted in the execution of task with equal distance in the same task, but different distances in other tasks. When faults occur, rollback to the latest checkpoint and re-execute task after the checkpoint. We derive the equation of maximum slack time for each task, and determine the number of re-executable checkpoint intervals for fault recovery. The equation to check the schedulibility of tasks is also derived. Based on these equations, we find the probability of all tasks executed within their deadlines successfully. Checkpoint intervals which make the probability maximum is the optimal.