Given its computational efficiency and versatility, belief propagation is the most prominent message passing method in several applications. In order to diminish the damaging effect of loops on its accuracy, the first explicit version of generalized belief propagation for networks, the KCN-method, was recently introduced. This approach was developed in the context of two problems: percolation and the calculation of matrix spectra. The KCN-method was then extended in order to deal with graphical models’ inference on networks. It was in this scenario where an improvement on the KCN-method, the NIB-method, was conceived. We show here that this improvement can also be achieved in the original applications of the KCN-method.