Localization is a critical issue in wireless sensor networks. In most localization schemes, there are beacons being placed as references to determine the positions of objects or events appearing in the sensing field. The underlying assumption is that beacons are always static. In this work, we define a new Beacon Movement Detection (BMD) problem. Assuming that there are unnoticed changes of locations of some beacons in the system, this problem is concerned about how to automatically monitor such situations and identify these beacons. Removal of such beacons in the positioning engine may improve the localization accuracy. Two schemes are proposed to solve the BMD problem. Finally, we evaluate how these solutions can improve the accuracy of localization schemes in case that there are unnoticed movement of some beacons. Simulation results show that our solutions alleviate 53% the decrease of positioning accuracy caused by the exceptional beacon movement.