Achieving optimum coordination of directional overcurrent relays is a very complicated task in the large interconnected system including huge numbers of relays. In the literature, various objective functions (OFs) are reported to obtain minimum operating time of relays and minimum prescribed discrimination time between the operations of primary and backup (P/B) relays. In this paper, the performance of five well-established OFs is examined, and in addition, a new OF is proposed to improve the previously proposed OFs. The proposed OF (POF) minimises operating time of P/B relays together with discrimination time between their operations. Also, the coordination problem is formulated considering near and far-end faults and solved by using a genetic algorithm. In order to evaluate the effectiveness, the POF is implemented over the IEEE 14-bus and IEEE 30-bus distribution networks, and obtained results are compared with those obtained by using previously proposed OFs presented in the literature.