In this correspondence paper, we investigate the problem of user scheduling in a cooperative non-orthogonal multiple access (NOMA) system consisting of a base station, a weak user, and K intermediate users. During each transmission, an intermediate user is scheduled to receive its own message and forward the message destined for the weak user. For this type of cooperative NOMA system, a novel scheduling scheme is proposed to achieve full diversity and scheduling fairness simultaneously. With the consideration that all channels experience independent but non-identically distributed Rayleigh fading, outage probabilities of the weak user and the scheduled intermediate user are derived in closed-form expressions. It is theoretically shown that the proposed scheme provides full diversity for both the weak user and the scheduled intermediate user. Furthermore, theoretical results also demonstrate that the proposed scheme schedules each intermediate user with the same probability 1/K, demonstrating that scheduling fairness is also guaranteed.