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In mobile networks, the location of a mobile user needs to be traced for successful and efficient call delivery. In existing cellular networks, as a mobile user changes his/her location area (LA), a location registration request is sent to the home location register (HLR) to update the user profile to point to the new LA. With a large number of mobile subscribers, this conventional registration strategy will incur a high volume of signaling traffic. We propose a new location registration strategy, called Group Registration (GR), which efficiently reduces the location registration cost by reporting location changes to the HLR for multiple mobile terminals (MTs) in a single location update request message. Specifically, the IDs of the MTs newly moving into an LA are buffered and sent to the HLR for location update in the route response message of the next incoming call to any MT in the LA. An analytic model is developed and numerical results are presented. It is shown that the proposed GR strategy can achieve significant cost reductions compared to the conventional strategy and the local anchor strategy over a wide range of system parameters. Moreover, the GR strategy results in a much smaller call delivery latency than the local anchor strategy.