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In modern collaborative and distributed applications, authenticated group key agreement (AGKA) is one of the important issues. In this paper, we present that one existing certificateless AGKA protocol has some security drawbacks and does not satisfy some security attributes required for AGKA protocols. To overcome its drawbacks, we propose a secure and efficient protocol upon the initial one and a signature scheme proved secure in the random oracle model. The security analysis shows that our improved protocol can achieve Explicit key authentication, Known session key security, Known ephemeral secrets security, Perfect forward security, No key compromise impersonation, No key control and No unknown key share. With respect to efficiency, our protocol only needs three communication rounds. In each protocol run, only three pairing computations are involved for each participant.