We obtain a structure theorem for the GCUD-Reciprocal LCUM matrices defined on S. If S is unitary divisor (ud)-closed, we calculate the determinant of the GCUD-Reciprocal LCUM matrix defined on S and show that it is positive definite. The set S is said to be unitary divisor (ud)-closed [Linear and Multilinear Algebra 41 (1996), 233-244] if all unitary divisors of any member of S belong to S. We obtain the trace and the value of the determinant of the GCUD-Reciprocal LCUM matrix defined on an arbitrary ordered set of distinct positive integers. If S is ud-closed, then we calculate the inverse of the GCUD-Reciprocal LCUM matrix