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This paper deals with a scheme for fault-tolerance improvement of real-time embedded systems, which engages an equidistant checkpointing technique to tolerate transient errors. Transient errors are caused by transient faults which are the most significant type of fault in reliable computer systems. Transient faults are assumed to occur according to a Poisson process and to be detected in a non-concurrent manner (e.g., checked periodically). The probability of the successful real-time task completion in the presence of transient errors is derived with the consideration of the possible effects of the transient errors. Based on this, a condition under which inserting checkpoints improves the fault-tolerance of the system is introduced and an optimal equidistant checkpointing strategy that achieves the highest fault tolerance is presented.