Major Wireless Sensor Network designs are focused on improving the network lifetime. The data aggregation process is the simplest way to achieve this. The PEGASIS routing protocol is a promising approach for efficient data aggregation in Wireless Sensor Networks. It is also reported in the literature that the PEGASIS performs better than LEACH and HEED protocol towards improving the network lifetime. However, in PEGASIS, the selection of a leader located far away from the base station still remains exposed to higher energy consumption for sending aggregated data. In this paper, we propose an enhancement to the chain formation process of PEGASIS to further improve its lifetime, and called it PEGASIS with Improved Network Lifetime (PEGASIS-INL). In contrast to original PEGASIS protocol, the PEGASIS-INL selects a node as a leader only if it is within a strong communication range of base station. A multiple overlapped chain formation and the aggregation technique is used for transmission of sensed information to the base station. Experimental results demonstrate that the PEGASIS-INL algorithm outperforms PEGASIS in terms of the product of consumed energy and delay, weighting the overall performance of both the energy consumption and the network lifetime.