Rate-monotonic scheduling algorithm is one of the most widely used scheduling strategies, for real-time systems. Since 1973, when it was first introduced, many researchers have studied its behavior and practical safety verification algorithms have been developed. In this paper, a possible modification to the traditional Rate-Monotonic (RM) algorithm is examined. Namely, by eliminating unnecessary preemption, processor utilization is well improved. Another less important result, due to this modification is that the number of context switching is decreased, which, in turn, reduces overhead time. The new scheduling strategy is called a preemption Intelligent Rate- Monotonic (IRM) algorithm. It is proved that a system of two tasks is safe if, and only if, the processor load factor is U£1. It has also been proved that any system that is safe with the rate-monotonic algorithm is also safe with the IRM algorithm.