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We consider a bidirectional relay system using a physical-layer network coding (PNC) protocol with Alamouti's space-time block coding (STBC) at the two source nodes while there is only one antenna at the relay node. Upper and lower bounds on symbol error probability (SEP) are derived for Binary Phase Shift Keying (BPSK) modulation scheme. It is shown that a diversity order of 2 can be achieved even that the relay node has only a single antenna. Simulation results are provided to confirm our analysis for the SEP.