The document proposes a new multiuser detection algorithm for CDMA based on the belief propagation algorithm. It develops a factor graph that represents the posterior distribution of information bits in a way that reduces the number of cycles compared to previous factor graphs. Numerical simulations show the proposed belief propagation algorithm outperforms the parallel interference canceller detector, especially for signature sequences that produce factor graphs with fewer cycles and weaker cross-correlations between users. The approach shows promise for application to other communication systems.