In this paper, we consider two-way amplify-and-forward relaying communication over a multiple relays network in which the best relay node is selected among others. Our proposed scheme picks for duplex communication between the source and the destination only the relay which provides the best end-to-end performance based on the instantaneous channel information. Similar to the relay selection method proposed in , our scheme also does not require any explicit communications among the relays. Based on the proposed relay selection criterion, we offer the performance bounds on the average sum-rate, average symbol error rate, outage probability over identically, independent distributed Rayleigh fading channels. Further, our numerical examples show that our proposed scheme provides considerable sum-rate gains and offers an increasing a diversity order as the number of relay candidates increases.