Mobile IP is supported by the latest wireless access technologies such as IEEE 802.16 Wireless Metropolitan Area Networks (WMANs), IEEE 802.11 Wireless Local Area Networks (WLANs), and High-Speed Downlink Packet Access (HSDPA). However, these access technologies are limited in deploying idle mode since the Mobile IP (MIP) was not developed considering the idle mode situation of wireless access networks. As a consequence, the idle mobile terminals (MTs) need make registration with home agent (HA) whenever they move to new foreign agents (FAs). This increases location update signaling cost between HA and FA despite that the idle MTs do not have any incoming or outgoing packets. Researchers have provided some solutions where location update signaling cost is still high. It is needed to minimize. Most of the existing solution is not efficient when arrival of packets is low or the terminal has very low residence time. Therefore we propose a mechanism where registration with the FA is conducted for an idle MT during the first packet arrival instance. We named this mechanism as Registration at First Packet Arrival instance (RFPA). In MIP domain location update signaling cost decreases significantly by using our proposed RFPA. Numerical results show the significance of our proposed solution.