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In this letter, we consider a half-duplex amplify-and-forward two-way relaying network consisting of two sources with each having a single antenna and one relay having two antennas. For such a system, a distributed orthogonal space-time block code (STBC) is proposed by making use of the Alamouti coding scheme and jointly processing the signals from the two antennas at the relay node. Such a code turns out to make the equivalent channel at each source node be a product of the two Alamouti channels and thus, is called distributed concatenated Alamouti STBC. In addition, the asymptotic formula of exact symbol error probability (SEP) for a quadrature amplitude modulation (QAM) constellation with the maximum likelihood (ML) detector is derived. This result shows that the full diversity gain function is achieved and proportional to ln SNR /SNR2.