Summary: A new class of ternary sequence with a zero-correlation zone is introduced. The proposed sequence sets have a zero-correlation zone for both periodic and aperiodic correlation functions. The proposed sequences can be constructed from a pair of Hadamard matrices of size n0n0 and a Hadamard matrix of size n1n1. The constructed sequence set consists of n0n1 ternary sequences, and the length of each sequence is (n1+1) for a non-negative integer m. The zero-correlation zone of the proposed sequences is |τ|≤ -1, where τ is the phase shift. The sequence member size of the proposed sequence set is equal to times that of the theoretical upper bound of the member size of a sequence set with a zero-correlation zone.