The present paper introduces a novel construction of structured ternary sequences having a zero-correlation zone (ZCZ) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation function of the proposed sequence set are zero for phase shifts within the ZCZ. The proposed ZCZ sequence set can be generated from an arbitrary Hadamard matrix of order n. The sequence set of order 0 is identical to the r-th row of the Hadamard matrix. For m≥0, the sequence set of order (m+1) is constructed from the sequence set of order m by sequence concatenation and interleaving. The sequence set of order m has 2^m subsets of size n. The length of the sequence is equal to n4^m+2^m+1(2^m-1); The phase shift of the ZCZ for the whole sequence set is from -(2^m-1) to (2^m-1). The sequence set of order 0 is coincident with the rows of the given Hadamard sequence with no ZCZ. The subsets can be associated with a perfect binary tree of height m with 2^m leaves. The r-th sequence subset consists of from the nr-th sequence to the ((n+1)r-1)-th sequence. The r-th subset is assigned to the r-th leaf of the perfect binary tree. For a longer distance between the corresponding leaves to the r-th and s-th sequences, the ZCZ of the r-th and s-th sequences is wider. This tree-structured width of ZCZ of a pair of the proposed sequences enables flexible design in applications of the proposed sequence set. The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth generation of radio access networks.