Clustering algorithm is an essential element to implement a hierarchical routing protocol, especially for a large-scale wireless sensor network. In this paper, we propose a new type of energy-efficient clustering algorithm, which maximizes the physical distance between cluster head and gateway by a neighbor node discovery mechanism. Furthermore, a slave/master patching scheme is introduced as a useful means of further improving the energy-efficiency. It has been shown that the number of cluster heads can be reduced by as many as 21% as compared with the existing clustering algorithms.