Information often comes from different sources and merging these sources usually leads to the apparition of inconsistencies. Fusion is the operation which consists in restoring the consistency of the merged information by changing a minimum of the initial information. In this paper, we are interested in linear constraints prioritized fusion in the framework of simple temporal problems (STPs). Priority expresses a preference relation between linear constraints and can represent either confidence or quality degrees of the constraints, or the reliability of their sources. We propose a local fusion method which we experiment on random prioritized STP instances.