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We investigate the outage performance of a two-phase two-way decode-and-forward (DF) relay channel in which each transceiver is equipped with two antennas, and uses the Alamouti orthogonal space-time block code (OSTBC) for transmission. The focus is on attaining good outage performance as enabled by the use of OSTBC transmissions in both phases, along with a low complexity near-optimum receiver in the first phase, and physical layer network coding (PNC) in the second phase. Assuming perfect channel state information at the receiver(s) in both phases, we derive expressions for the probability distribution functions of the signal-to-noise ratio (SNR) for all links in a Rayleigh flat-fading scenario. More precisely, we derive an exact expression of the outage probability for the end-to-end transmissions. The accuracy of the derived outage expression is verified by simulation results. We also demonstrate the impacts of channel asymmetry on the outage behavior. Numerical results show that the proposed scheme provides good performance under symmetric channel conditions.