Distributed space-time codes (DSTC) are often used in cooperative relaying networks whose relays can support a single antenna due to the limited physical size. In this paper, full DSTC protocol in which there is a data exchange between relays before forwarding signals to destination is proposed to improve the performance of a cooperative relaying system. A lower bound for the average symbol error probability (ASEP) of full DSTC cooperative relaying system in a Rayleigh fading environment is provided. In the case when the Signal to Noise Ratio (SNR) of the relay-relay link is much greater than that of the source-relay link, the upper bound on ASEP of this system is also derived. From the simulations, we show that the average SNR gain of full DSTC system over DSTC system is 3.8dB and the maximum SNR gain is 5dB when the relay-relay distance is small and the relays are in the middle of the source and the destination. The effect of the distance between the relays shows that the performance does not degrade so much as the distance between relays is lower than a half of the source-destination distance. Moreover, we also show that when the error synchronization range is lower than 0.5, the impact of the transmission synchronization error of the relay-destination link on the performance is not considerable.