The present paper introduces a novel construction of ternary sequences having a zero-correlation zone. The cross-correlation function and the side-lobe of the auto-correlation function of the proposed sequence set is zero for the phase shifts within the zero-correlation zone. The proposed sequence set consists of more than one subset having the same member size. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a wider zero-correlation zone than that of the correlation function of sequences of the same subset (intra-subset correlation function). The wide inter-subset zero-correlation enables performance improvement during application of the proposed sequence set. The proposed sequence set has a zero-correlation zone for periodic, aperiodic, and odd correlation functions.