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In Cognitive Radio (CR) communication, there exists a scenario that some users are located within No-Talk-Zone, thus they cannot maintain CR communication and avoid interference with primary system at the same time. In this scenario, the traditional transmit power control scheme becomes less effective. To address this issue, we propose a multiplex transmission scheme using both underlay and overlay transmission scheme, and we also consider the cooperation and power allocation between CR users. The key feature of the new transmission scheme is that CR user can communicate with CR receiver even if it is very close to the primary receiver. The achievable rate of a cognitive user under multiplex transmission scheme is simulated and analyzed, the simulation results demonstrate that the transmission rate of the proposed scheme is higher than that of underlay transmission scheme.