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MOTIVATION In the modeling of biological systems by Boolean networks a key problem is finding the set of fixed points of a given network. Some constructed algorithms consider certain structural properties of the regulatory graph like those proposed by Akutsu et al. (1998b); Zhang et al. (2007) which consider a feedback vertex set of the graph. However, these methods do not take into account the type of action (activation, inhibition) between its components. RESULTS In this paper we propose a new algorithm for finding the set of fixed points of a Boolean network, based on a positive feedback vertex set P of its regulatory graph and which works, by applying a sequential update schedule, in time O(2 |P| · n2+k), where n is the number of components and the regulatory functions of the network can be evaluated in time O(nk), k ≥ 0. The theoretical foundation of this algorithm is due a nice characterization, that we give, of the dynamical behavior of the Boolean networks without positive cycles and with a fixed point. AVAILABILITY AND IMPLEMENTATION An executable file of FixedPoint algorithm made in Java and some examples of input files are available at: www.inf.udec.cl/~lilian/FPCollector/. SUPPLEMENTARY INFORMATION Supplementary material is available at Bioinformatics online.