Throughout the paper, G will denote an additively written, but not always abelian, group of finite order n; and X = (xij) will denote a square matrix of order n with entries from G and whose rows and columns are numbered 0, 1, …, n − 1. We call X a cartesian array (afforded by G) if(1.1) The sequence {−xmi + xki, i = 0,…, n – 1} contains all elements of G whenever k ≠ m.By a theorem of Jungnickel (see Theorem 2.2 in [5]), the transpose of a cartesian array is also a cartesian array. We call G a cartesian group if there is a cartesian array X afforded by G. In this case, we also call (G, X) a cartesian pair.