Cooperation diversity schemes employing space-time block coding (STBC) techniques have been proposed for wireless networks to increase network capacity and coverage even when each node is equipped with a single antenna. Such schemes allow several relay stations distributed in space to assist the transmission between a given source-destination pair. A key design problem in cooperative networks is to take advantage from spatial diversity by reducing the amount of signaling and processing overhead as far as possible. In this paper, capitalizing on randomized STBC (RSTBC), a coding method which has been recently developed for decode-and-forward (D&F) relay nodes, a totally decentralized cooperative communication scheme is proposed for amplify-and-forward (A&F) relays, where each relay is unaware of both the effective STBC being employed by the other nodes and the number of cooperating stations. Numerical results are provided to highlight the effectiveness of the proposed scheme in comparison to its D&F counterpart.