This paper introduces a range map stitching (RMS) algorithm for localizing sensor nodes in wireless sensor networks dealing with non-line-of-sight (NLOS) conditions, which typically hinder localization accuracy. It demonstrates that the RMS algorithm improves localization precision and energy efficiency compared to existing methods by mitigating NLOS errors through a two-step process of creating and iteratively stitching local maps. Simulations validate the algorithm's performance across various scenarios, showcasing its effectiveness in achieving reliable node localization.