Localization in wireless sensor networks is essential to important network functions such as event detection, geographic routing, and information tracking. Localization is to determine the locations of nodes when node connectivities are given. In this paper, centroid approach known as a distributed algorithm is extended to a centralized algorithm. The centralized algorithm has the advantage of simplicity. but does not have the disadvantage that each unknown node should be in transmission ranges of three fixed nodes at least. The algorithm shows that localization can be formulated to a linear system of equations. We mathematically show that the linear system have a unique solution. The unique solution indicates the locations of unknown nodes are capable of being uniquely determined.