The low-power technology is the most important technology required to prolong the network lifetime of wireless sensor network with limited resources. Especially, reducing redundant message transmission and unnecessary communication participation is the core of the low-power wireless sensor network. The Directional Messaging (DM) protocol is the energy efficient message protocol which reduces unnecessary communication participation by sending messages with directional information only to the specified area in a network. However, there is the problem in the DM that the border nodes of search areas receive and send redundant messages. In this paper, we propose the non-redundant directional messaging protocol which improves the energy efficiency of wireless sensor network by reducing redundant message transmission on the border nodes of search areas in the DM protocol. We also show the improved energy efficiency of the proposed protocol comparing with the Directed-Messaging protocol by the simulated results using NS-2 simulator.