We formulate a problem of goal satisfaction in mutex networks in this paper. The proposed problem is motivated by problems that arise in concurrent planning. For more efficient solving of goal satisfaction problem we design a novel global filtration technique. The filtration technique is based on exploiting graphical structures of the problem - clique decomposition of the problem is used. We evaluated the proposed filtration technique on a set of random goal satisfaction problems as well as a part of GraphPlan based planning algorithm. In both cases we obtained significant improvements in comparison with existing techniques.