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Round robin based packet schedulers generally have a low complexity and provide long-term fairness. The main limitation of such schemes is that they do not support short-term fairness. In this paper, we propose a new low complexity round robin scheduler, called Fair Round Robin (FRR), that overcomes this limitation. FRR has similar complexity and long-term fairness properties as the stratified round robin scheduler, a recently proposed scheme that arguably provides the best quality-of-service properties among all existing round robin based low complexity packet schedulers. FRR offers better short-term fairness than stratified round robin and other existing round robin schedulers.