This article proposes a new space-time cooperative diversity scheme called full feedback-based cooperative diversity scheme (FFBCD). In contrast to the conventional adaptive space-time cooperative diversity schemes that utilize the feedback from only the destination node, the new scheme utilizes the feedback from both the destination node and the cooperation node. With the feedback from the destination node, the occasional successful reception of the destination node in the information distribution stage can be detected, thus avoiding unnecessary retransmissions in the information delivery stage. The feedback from the cooperation node indicates the receiving state of the cooperation node in the information distribution stage, and the source node and the cooperation node will not perform cooperative retransmission during the information delivery stage unless the cooperation node is received successfully in the information distribution stage. In this way the new scheme can reduce the number of transmission attempt and improve the channel utilization. The expressions of the average number of transmission attempt are given. Numerical approximations and simulation results both show that the new scheme performs better than the non-cooperative scheme and the conventional adaptive space-time cooperative diversity scheme.