Wireless sensor network (WSN) is one of popular research issues, and ZigBee is an important protocol for WSN. Traditionally, the device addresses in WSN are given by a Distributed Address Allocation Mechanism (DAAM). Although DAAM has better extensibility, this network topology resulted by DAAM did not consider fast routing between nodes. Although binary tree topology benefits a faster packet routing via a simple Boolean computation, the binary tree is less extensible. In this paper, a new variation of binary tree topology is proposed to assign nodes under routers the addresses for fast routing. The proposed approach improves the low utility rate of the network address for DAAM.