In this paper, we introduce a bit-interleaved binary space-time code (B-STC) for a coded multiple-input multiple-output (MIMO) system to obtain an additional diversity gain over the full-rate spatial multiplexing (SM) transmission. By applying the B-STC scheme, codeword bits from each stream are transmitted effectively through N-t or (N-t - 1) layers in N(r)xN(t) MIMO systems. At the receiver, the iterative decoding is performed. The extrinsic information provided by the soft-in/soft-out (SISO) decoder is applied as an improved priori information after the B-STC decoding at the next iteration. Since a priori information can be extracted from multiple layers independently by the B-STC scheme, codeword bits have an improved diversity gain of (N-t-1). In order to verify the proposed scheme, we derive the asymptotic bit error probability, which can be achieved after convergence of the iterative decoder. Because the proposed B-STC scheme is a binary code for coded MIMO systems, different types of channel codes and various space-time codes can be also concatenated.