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It is the scheduler that decides the capability of the embedded system. For the classical rate-monotonic (RM) scheduling algorithm with priority determined only by the period, the deadline of long period tasks can not be guaranteed and the system resources can not be effectively utilized. Here, a new static priority scheduling algorithm called NPRM (a new priority-driven scheduler based on RM) is proposed. In this algorithm, two parameters are added to the task control block (TCB): One is the importance of the task, and the other is the laxity. The one which importance is higher only when its laxity is zero could preempt the running task. Our experiments suggest that the algorithm be capable of decreasing the deadline-missing ratio of the tasks and the CPU resource could be used more effectively. It is an efficient way of scheduling the real-time tasks; it is useful for the application in wireless broadband and mobile computing.