The general approach to fault tolerance in uniprocessor systems is to maintain enough time redundancy in the schedule so that any task instance can be re-executed in presence of faults during the execution. In this paper a scheme is presented to add enough and efficient time redundancy to the Earliest-Deadline-First (EDF) scheduling policy for periodic real-time tasks. This scheme can be used to tolerate transient faults during the execution of tasks. We describe a recovery scheme which can be used to re-execute tasks in the event of transient faults and discuss conditions that must be met by any such recovery scheme. For performance evaluation of this idea a tool is developed.