Due to hardware and computational constraints, wireless sensor networks (WSNs) normally do not take measurements of time-of-arrival or time-difference-of-arrival for range-based localization. Instead, WSNs in some applications use range-free localization for simple but less accurate determination of sensor positions. A well-known algorithm for this purpose is the centroid algorithm. This paper presents a range-free localization technique based on the radical line of intersecting circles. This technique provides greater accuracy than the centroid algorithm, at the expense of a slight increase in computational load. Simulation results show that for the scenarios studied, the radical line method can give an approximately 2 to 30% increase in accuracy over the centroid algorithm, depending on whether or not the anchors have identical ranges, and on the value of DOI.