This paper presents a new algorithm for fixed-priority scheduling of sporadic task systems on multiprocessors. The algorithm is categorized to such a scheduling class that qualifies a few tasks to migrate across processors, while most tasks are fixed to particular processors. We design the algorithm so that a task is qualified to migrate, only if it cannot be assigned to any individual processors, in such a way that it is never returned to the same processor within the same period, once it is migrated from one processor to another processor. The scheduling policy is then conformed to DeadlineMonotonic. According to the simulation results, the new algorithm significantly outperforms the traditional fixed-priority algorithms in terms of schedulability.