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The most important and integral part of a computer system is its operating system. Scheduling various resources is one of the most critical tasks an operating system needs to perform. Process scheduling being one of those tasks, involves various techniques that define how more than one processes can be executed simultaneously. The primary aim here is to the system more efficient and faster. The fundamental scheduling algorithms are: First Come First Serve (FCFS), Round Robin, Priority Based Scheduling, and Shortest Job First (SJF). This paper focuses on Round Robin Scheduling algorithm and various issues related to it. One major issue in RR scheduling is determining the length of Time Quantum. If the Time Quantum is too large RR scheduling behaves as FCFS. On the other hand, if it is too small it forces considerable increase in the number of context switches. Our main objective is to overcome this limitation of traditional RR scheduling algorithm and maximize CPU utilization, further, leading to more efficient and faster system. Here we propose an algorithm that categorizes available processes into High Priority processes and Low Priority process. The proposed algorithm reduces the average waiting time of High Priority processes in all cases and of Low Priority processes in not all but some cases. The overall waiting time changes on the basis of set of processes considered. The simulation results justify that the proposed schemes reduces the overall average waiting time when compared to the existing schemes.