Cooperative diversity is a technique with which a virtual multiple antenna array is established among the single antenna users of the wireless network to realize space diversity. Signal space diversity (SSD) is a bandwidth-efficient diversity technique, which uses constellation rotation and interleaving techniques to achieve diversity gain. A new cooperative diversity scheme with rotated constellations (RCCD) is proposed in this paper. In this scheme, data are modulated by using a rotated constellation, and the source and the relays transmit different components of the modulated symbols. Since any one of the components contains full information of the symbols, the destination can obtain multiple signals conveying the same information from different users. In this way, space diversity is achieved. The RCCD scheme inherits the advantage of SSD - being bandwidth-efficient but without the delay problem of SSD brought by interleaving. The symbol error rate of the RCCD scheme is analyzed and simulated. The analysis and simulation results show that the RCCD scheme can achieve full diversity order of two when the inter-user channel is good enough, and, with the same bandwidth efficiency, has a better performance than amplify-and-forward and detect-and-forward methods.