The efficiency of group key management is a key issue in secure group communications, since the group key must be renewed each time the group membership changes. This paper examines the performance of a periodic rekeying technique for the key management of groups that exhibit bursty behaviour. Experimental results demonstrate that this technique costs far fewer key generations than existing approaches, and is therefore more efficient in terms of computation. When the pre-processing of joining members can be performed during the rekeying period, this technique reduces the rekeying time at the end of the rekeying period to the lower bound.