In this article, we present a construction of low correlation zone (LCZ) sequence sets. This construction gives a new class of quaternary LCZ sequence sets. Furthermore, we observe a generalization of the LCZ sequence sets in Kim et al. (IEEE Trans Inform Theory 52(10):4607-4616, 2006) by using an orthogonal transformation. The obtained LCZ sequence sets are optimal with respect to the Tang, Fan and Matsufuji bound.