Many varieties of regular languages have characterizations in terms of forbidden-patterns of their accepting finite automata. The use of patterns while inferring languages belonging to those families through the RPNI-Lang algorithm help to avoid overgeneralization in the same way as negative samples do. The aim of this paper is to describe and prove the convergence of a modification of the RPNI-Lang algorithm that we call FCRPNI. Preliminary experiments done seem to show that the convergence when we use FCRPNI for some subfamilies of regular languages is achieved faster than when we use just the RPNI algorithm.