This paper presents an optimal checkpoint strategy for fault-tolerance in real-time systems where transient faults occur in Poisson distribution.In our environment,multiple real-time tasks with different deadlines and harmonic periods are scheduled in the system by rate-monotonic algorithm,and checkpoints are inserted at a constant interval in each task.When a fault is detected,the system carries out rollback to the latest checkpoint and re-executes tasks.The maximum number of re-executable checkpoints and an equation to check schedulability are derived,and the optimal number of checkpoints is selected to maximize the probability of completing all the tasks within their deadlines.