A sensor network is composed of a large number of sensor nodes that are densely deployed in a field. Each sensor performs a sensing task for detection specific events. After detecting this event, location information of the sensor node is very important. Range-based scheme of the proposed approaches typically achieve high accuracy on either node-to-node distances or angles, but this scheme have a drawback because all sensor nodes have the special hardware. On the other hand, range-free scheme provides economic advantage because of no needed hardware even if that leads to coarse positioning accuracy. In this paper, we propose a range-free localization algorithm without range information in wireless sensor networks. This is a range-free approach and uses a small number of anchor nodes and known sensor nodes. This paper develops a localization mechanism using the geometry conjecture (perpendicular bisector of a chord). The conjecture states that a perpendicular bisector of a chord passes through the center of the circle.