In this paper, we develop a new class of orthogonal Latin hypercubes (OLHs) based on Latin squares. These OLHs have n = 2(r+1) + 1 rows and k = 2(r) columns (r = 1, 2, . . .). For a given number of runs, our OLH vastly increases the numbers of orthogonal columns of OLHs in Ye (1998) and Cioppa & Lucas (2007).