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The main aim of this paper is to propose a new approach for round robin scheduling which helps to improve the performance of CPU in real time and time sharing operating system. Existing CPU scheduling algorithm cannot be implemented in real time operating system due to their high context switch rates, large waiting time, and large response time, large turnaround time and less throughput. The proposed algorithm improves all the drawbacks of round robin scheduling algorithm. The paper also presents the comparative analysis of proposed algorithm with existing round robin scheduling algorithm.