In this paper, we propose a range-free localization method that can improve the estimation accuracy of Approximate Point in Triangle(APIT), which is the representative localization method for low cost wireless sensor networks. Specifically, we propose extended-APIT(e-APIT) method, which minimizes the error in deciding whether an object is in an area formed by three beacons. We also propose a way to improve the localization by narrowing down the potential localization area using the signals from neighboring beacons. According to the simulation performed, the proposed e-APIT method demonstrated noticeable accuracy improvement over the conventional APIT method.