This paper is aimed at studying fault-tolerant design of the realtime multi-processor systems and is in particular concerned with the dynamic mapping and scheduling of tasks on embedded systems. The effort is concentrated on scheduling strategy having reduced complexity and guaranteeing that, when a task is input into the system and accepted, then it is correctly executed prior to the task deadline. The chosenmethodmakes use of the primary/backup approach and this paper describes its refinement based on reduction of windows within which the primary and the backup copies can be scheduled. The results showthat the use of restricted scheduling windows reduces the algorithm complexity by up to 15%.