A closed form average irreducible bit error rate (AIBER) expression for space-time block coding (STBC) in frequency selective Rayleigh fading channel is derived using the probability distribution of the general quadratic form. A 2 tx/1 rx antenna pair and BPSK modulation are assumed. We extended Alamouti's decoding algorithm, which is optimum in the flat fading channel, to the frequency selective fading scenario. Our result provides an efficient way to evaluate the effects of selective fading with various forms of power delay profiles (PDP) and pulse shaping on error rate performance of STBC. This is a significant improvement over previous simulation based approach.