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In cognitive radio where continuous spectrum monitor is required, primary user detections should be performed successively. As the primary user usually keeps absent/present for some time, its states (absence or presence) at successive detections are not independent with each other. In this paper, a novel detection scheme is proposed to exploit the relation among them. At the beginning of each detection, this scheme exploits the relation by deriving instantaneous a priori probabilities from previous detections' results. Then using these probabilities, Bayesian cost of both false alarm and missed detection is minimized. Simulation results are also provided in this paper, showing that the proposed scheme is not only better than classical energy detection scheme, but also superior to the Bayesian energy detection scheme that does not exploit the relation and minimizes Bayesian cost only with average a priori probabilities.