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This letter studies the application of non-orthogonal multiple access to a downlink cognitive radio (termed CR-NOMA) system. A new cooperative transmission scheme is proposed aimed at exploiting the inherent spatial diversity offered by the CR-NOMA system. The closed-form analytical results are developed to show that the cooperative transmission scheme gives better performance when more secondary users participate in relaying, which helps achieve the maximum diversity order at secondary user and a diversity order of two at primary user. The simulations are performed to validate the performance of the proposed scheme and the accuracy of the analytical results.