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Cognitive Radios allow secondary users to share the spectrum with primary users. The fairness between secondary users in Cognitive Radio networks is an important issue. This paper analyzes the fairness based on the distributed opportunistic spectrum access scheme. A fair multiple access scheme using fast catch-up strategy is proposed. The theoretical result of the first passage time to achieve fairness is given. Simulation results demonstrate that the Fair OSA scheme can achieve fairness much faster when a new secondary user accesses the spectrum. A complex practical scenario is simulated to validate the fairness in more general situations.