The present paper introduces a novel type 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 pair of an Hadamard matrix of order l_h and a binary/ternary perfect sequence of length l_p. 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 has l_p subsets of size 2l_h. The periodic correlation function and the aperiodic correlation function of the proposed sequence set have a zcz from -(2^m+1-1) to 2^m+1-1. The periodic correlation function and the aperiodic correlation function of the sequences of the i-th subset and k-th subset have a zcz from -2^m+2-(l_h+1)((j-k) mod l_p) to -2^m+2-(l_h+1)((j-k) mod l_p). The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth-generation mobile networks.