The random coding exponent of multiple antenna systems using space time block codes (STBC) was studied. The effects of different choices of STBC's on the overall performance of a antenna system was analyzed. A narrow band, block fading, multiple antenna channel with N_t antennas at the transmitter and N_r antennas at the receiver were considered for the analysis. The STBC symbols were transmitted across the channel using maximum likelihood, ML, sequence detection. The random coding exponent were found for the cases N_r = 1 and 2. It was concluded that by properly designing the inner STBC the length of the outer code could be reduced while maintaining some target error probability.