Most of the local search methods for the satisfiability problem deal with a complete and inconsistent truth as- signment of the problem variables, and try to repair it by switching the truth value of some variables until reaching a model. We propose a new local search algorithm which works on partial truth assignments, but always consistent, instead of complete and inconsistent ones. This method at- tempts to extend a current partial assignment as a complete method would do. However, instead of backtracking when a conflict arises, it frees at least one variable involved in each falsified clause to restore consistency. Thus, the ex- plored neighborhood is always consistent whereas it is not the case for classical local search algorithms. Experimen- tal results show the competitiveness of our method towards other local search methods.