The rate monotonic scheduling algorithm is a commonly used task scheduling algorithm for periodic realtime task systems. This paper discusses feasibility decision for a given real-time task system by the rate monotonic scheduling algorithm. It presents a new necessary and suficient condition for a given task system to be feasible, and a new feasibility decision algorithm based on that condition. The time complexity of this algorithm depends solely on the number of tasks. This algorithm can be applied to the inverse-deadline scheduling algorithm, which is an extension of the rate monotonic scheduling algorithm.