Important inference problems in computer vision, error-correcting coding theory, and artificial intelligence can all be formulated as the computation of marginal probabilities on factor graphs. We focus on the Belief Propagation (BP) Algorithm, which is an efficient way for solving inference problems based on passing local messages. Belief Propagation Algorithm is exact only when the factor graph is a tree. Convergence and accuracy cannot be guaranteed for a general graph. We propose a method for improving BP that takes into account the influence of cycles in the factor graph. We prove its convergence and exactness for a single cycle and are working towards generalizing the approach.