In this paper we investigate the performance of two-way relaying that uses Alamouti space-time block code (STBC) and network coding. In this scheme, two nodes use Alamouti STBC to transmit their symbols to the relay consecutively in two phases. The relay detects and demodulates the transmitted symbols from the nodes, and then uses the bitwise-XOR operation to combine the detected bits. Then the relay modulates and broadcasts the XORed bits to the nodes using Alamouti STBC. In this paper, the bit error rate of the proposed scheme is derived for an uncorrelated Rayleigh fading channel with perfect channel estimation at receivers.