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The primary function of the Internet protocol (IP) is delivering datagram's across an internetwork and addressing is one of the most important functions of IP. Communication between hosts over an internetwork is accomplished using IP addresses, but the actual communication over a physical network takes place using physical addresses. The mapping of IP addresses to physical addresses is done through address resolution methods. As address resolution is performed at each hop along the path through the Internet, efficiency of this process is of concern. In IP, address resolution queries and responses consume bandwidth, and end nodes are forced to waste CPU cycles receiving and discarding address resolution queries for other nodes which is an overhead. This paper explores the possibility of improving the performance of IPv6 packet transmission through the use of an efficient address resolution method. The performance of application processes depends on the throughput of the server and network. The throughput of a server depends on its processing power and load while the throughput of a network is directly influenced by the efficiency of routers, switches and bandwidth used. This paper proposes to use address resolution through direct mapping instead of dynamic binding which would enhance the efficiency of the address resolution process and plausibly improve the performance of IPv6 packet transmission.