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Many earlier works have studied the problem of cooperative spectrum sensing in cognitive radio networks. However, relay selection was not considered which can improve the performance of cooperative communication systems. In this paper, the detection probability and false alarm probability are evaluated when relay selection is executed for cooperative spectrum sensing in cognitive radio networks. The cognitive radio network consists of a primary user and multiple cognitive users. A cognitive user tries to detect the primary signal. The other cognitive users assist the transmission from the primary user to that cognitive user. The relay selection scheme is that the relay with maximum SNR on its path is selected. Numerical simulations are conducted to compare the results with those corresponding to direct transmission. It is shown that the diversity gain achieved by the relay selection scheme depends on the channel gains as well as the decision threshold which is a critical parameter in cognitive radio systems.