Fuzzy Cognitive Maps are network-like decision support tools, where the final conclusion is determined by an iteration process. Although the final conclusion relies on the assumption that the iteration reaches a fixed point, it is not straightforward that the iteration will converge to anywhere, since it can produce limit cycles or chaotic behaviour also. In this paper, we briefly analyse the behaviour of the so-called rescaled algorithm for fuzzy cognitive maps with respect to the existence and uniqueness of fixed points.