Since Time synchronization is also critical in Wireless Sensor Networks (WSN) like other networks, a time synchronization protocol for WSN called IBS(Indirect-Broadcast Synchronization) has been already proposed in 2012. As IBS operates in cluster tree topology, network lifetime may be mainly shortened by cluster head node[s], which usually consumes more power than cluster member (i.e. non-cluster head) nodes. In this paper, I propose enhanced version of IBS (called EIBS) which saves overall energy and prolongs network lifetime by re-constructing partial cluster tree locally. Compared with other tree construction approaches, this tree reconstruction algorithm is not only simpler, but also more efficient in the light of overall power consumption and network lifetime.