Efficient energy consumption in WSN is one of the key design issues for improving network stability period. In this paper, we propose a new Heterogeneity-aware Energy-efficient Clustering (HEC) technique which considers two types of heterogeneity - network lifetime and of sensor nodes. Selection of cluster head nodes is done based on the three network lifetime phases: only advanced nodes are allowed to become cluster heads in the initial phase; in the second active phase all nodes are allowed to participate in cluster head selection process with equal probability, and in the last dying out phase, clustering is relaxed by allowing direct transmission. Simulation-based performance analysis of the proposed technique as compared to other relevant techniques shows that HEC achieves longer stable region, improved throughput, and better energy dissipation owing to judicious consumption of additional energy of advanced nodes. On an average, the improvement observed for stability period over LEACH, SEP, FAIR and HEC- with SEP protocols is around 65%, 30%, 15% and 17% respectively. Further, the scalability of proposed technique is tested by varying the field size and number of sensing nodes. The results obtained are found to be quite optimistic. The impact of energy heterogeneity has also been assessed and it is found to improve the stability period though only upto a certain extent.