The basic real-time scheduling algorithms based on RM or EDF approaches assume that the tasks are preemptive, but the tasks may contain nonpreemptive sections in many cases. Also the existing scheduling algorithm for reducing the power consumption of the processor is based on the task utilizations and determines the processor speed $S_H$ or $S_L$ according to the existence of the blocking intervals. In this algorithm, the $S_H$ interval that operates in high speed is the interval during which the priority inversion by blocking occurs, and the length of this interval is set to the task deadline that includes the blocking intervals. In this paper, we propose an improved algorithm that can reduce the power consumption ratio by shortening the length of the $S_H$ interval. The simulation shows that the power consumption ratio of the proposed algorithm is reduced as much as 13% compared to the existing one.