Let S ＝ {x1, x2,...,xn} be a set of distinct positive integers. The n × nmatrix (S) whose i,j-entry is the greatest common divisor (xi, xj) of xi and xj is called the GCD matrix on S. A divisor d of x is said to be a unitary divisor of x if (d, x/d)=1.The greatest common unitary divisor (GCUD) matrix (S**) is defined analogously. We show that if S is both GCD-closed and GCUD-closed, then det(S**)≥det(S), where the equality holds if and only if (S**) = (S).