In the wireless sensor networks composed of battery-powered sensor nodes, one of the main issues is how to save power consumption at each node. The usual approach to this problem is to activate only necessary nodes (e.g., those nodes which compose a backbone network), and to put other nodes to sleep. One such algorithm using location information is GAF (Geographical Adaptive Fidelity), and the GAF is enhanced to HGAF (Hierarchical Geographical Adaptive Fidelity). In this paper, we show that we can further improve the energy efficiency of HGAF by modifying the manner of dividing sensor-field. We also provide a theoretical bound on this problem.