The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone (ZCZ), which is referred to as a ZCZ sequence set. The proposed sequence construction generates a ZCZ sequence set from a ZCZ sequence set. The proposed method can generate an almost optimal ZCZ sequence set, the member size of which approaches the theoretical bound, when an almost optimal ZCZ sequence is used for the sequence construction. The proposed sequence set consists of N₀ subsets, where a ZCZ sequence set Z(L₀, N₀, Z₀) is used in sequence construction. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a ZCZ with a width that is about $\left(1+\slenplusone\left(\frac{1}{\coef}+m\right)\right)$ times that of the correlation function of sequences of the same subset (intra-subset correlation function) for integers Λ≥1, T≥1, and m≥0. Wide inter-subset zero-correlation enables improved performance during application of the proposed sequence set.