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In this paper, we analyze the performance of ST-BICM (space-time bit-interleaved coded modulation) system employing the arbitrary constellation in quasi-static fading channels. We derive a new upper bound of the frame error probability of the system, which depends only on the product measure. In order to get the product measure, we analyze the type of error sequence, which is defined as the density spectrum of the constituent symbols that yield a certain number of bit errors. The analysis is based on the uniform interleaving, so we average the frame error probability over all possible interleavers. We also derive the statistical distribution of the product measure. Finally, we show that the new upper bound helps to predict the performance of the ST-BICM system with an arbitrary constellation.