This paper describes the system of unrestricted cognatic descent on the Polynesian island of Niutao. It addresses the controversy in anthropology concerning whether unrestricted cognatic descent groups can function as corporate groups with overlapping membership. Niutao descent groups are cognatic, overlapping, exogamous, and corporate. While these groups cannot handle the large array of functions of unilineal groups, the few functions they do handle are nevertheless important ones. [cognatic descent, corporations, descent theory. Polynesia]