A pair of sign pattern row vectors (respectively

column vectors) allows orthogonality if the two vectors are the sign patterns of two real orthogonal row vectors (respectively

column vectors). A square sign pattern matrix that does not have a zero row or zero column is sign potentially orthogonal (SPO) if every pair of rows and every pair of columns allow orthogonality. In this paper

we prove that when n is even

there is a k-regular SPO sign pattern of order n if and only if 1≤k≤n; when n≠5 is odd

there is a k-regular SPO sign pattern of order n if and only if 1≤k≤n and k≠2; when n=5

there is a k-regular SPO sign pattern of order n if and only if k≠2 and k≠3.