An unranking algorithm for a finite set Sis an algorithm that, given a number in {0, 1, ..., |S| -1}, returns an element of Sthat is associated with the number. We suppose that a number can be associated with any element in Sso long as distinct elements are associated with different numbers. A ranking algorithm is the reverse of an unranking algorithm. In this paper, we present an unranking algorithm for the set of all m-element subsets of an n-element set. Our algorithm runs with O(m3m+3)arithmetic operations, which is independent of nand hence is effective when nis large. We also show that it admits a ranking algorithm with the same running time.