Cooperative diversity has been recently proposed as a way to form distributed antenna arrays that improve error performance and capacity. In this paper, a bandwidth efficient cooperative diversity scheme is proposed for half-duplex amplify-and-forward wireless relay networks. By employing a signal space diversity technique and allowing the source node to keep on transmitting over the whole duration of the cooperation frame, the proposed cooperative scheme is proved to be able to achieve both full-rate and full-diversity simultaneously. Diversity analysis shows that the achievable diversity gain is M + 1, where M is the number of relay nodes. Moreover, a power allocation scheme is proposed to maximize the coding gain under a total power constraint. Simulation results are shown to demonstrate the full-rate and full-diversity of the proposed scheme.