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In IP Multimedia Subsystem (IMS) of UMTS, both packet-switch domain and IMS authentications are necessary for the IMS subscriber, so-called the two-pass authentication. However, the IMS authentication is carried out by IMS authentication and key agreement (IMS AKA). Since IMS AKA is based on 3GPP AKA that is used to Packet-switch domain authentication, almost all of the operations are the same. It is inefficient that almost all involved steps in the two-pass authentication are duplicated. Hence, Lin et al.'s proposed the one-pass authentication to increase efficiency of the IMS authentication. Unfortunately, in addition to some security problems, the one-pass authentication procedure only has unilateral authentication without capabilities of mutual authentication and key agreement. Therefore, this paper proposes an one-pass AKA procedure, which not only avoids the lacks of the one-pass authentication procedure but also does not lose the efficiency.