In Multiple-Input Multiple-Output (MIMO) wireless systems, the receiver must extract each transmitted signal from received signals. An iterative signal detection with Belief Propagation (BP) is an attractive technique for MIMO systems. This technique can improve the error rate performance with increasing the number of detection and decoding iterations. This number is, however, limited in actual systems because each additional iteration increases the latency, receiver size, and so on. This paper proposes a convergence acceleration technique that can achieve better error rate performance with fewer iterations than the conventional iterative signal detection. Since the Log-Likelihood Ratio (LLR) or a probability of one bit propagates to all other bits with BP, improving some LLRs improves overall decoder performance. In our proposal, all the coded bits are divided into groups and only one group is detected in each iterative signal detection whereas in the conventional approach, each iterative signal detection run processes all coded bits, simultaneously. Our proposal increases the frequency of initial LLR update (for BP) by increasing the number of iterative signal detections and decreasing the number of coded bits that the receiver detects in one iterative signal detection. Computer simulations show that our proposal achieves better error rate performance with fewer detection and decoding iterations than the conventional approach.