When a Graeco-Latin square is viewed as a pair of orthogonal Latin squares, each of the Latin squares is said to have an "orthogonal mate". In an arbitrary Latin square, a selection of positions, one in each row and one in each column whose entries are all distinct is called a "transversal" of that square. Consider one symbol in a Graeco-Latin square. The positions containing this symbol must all be in different rows and columns, and furthermore the other symbol in these positions must all be distinct. Hence, when viewed as a pair of Latin squares, the positions containing one symbol in the first square correspond to a transversal in the second square (and vice versa).