The most familiar fact about the Sumerian system of numeration is that it was based on the number sixty, very much as ours is based on the number ten: thus just as our words twenty and thirty etymologically signify 2X10 and 3 X 10, so did the Sumerian words gesh-min and gesh-esh signify 60 X 2 and 60 X }. But while with us the number words up to the larger unit ten are independent words, the Sumerian words up to sixty are, in most cases, composite forms; for this reason the Sumerian system has also been called decimal. The object of the present note is to show that that is not so. The argument will rest to a large extent on a simple examination of the Sumerian number system. As, however, recognized authorities have called the system decimal, we hope that our remarks will be helpful in correcting this misconception. Let us quote a few of these authorities. F. Thureau-Dangin (Esquisse d'une Histoire du Systeme Sexagesimal, p. 17), after commenting on the Sumerian number words up to ten, says: "With u '10', the system takes the decimal form." On the next page he says: "The genesis of the decimal system is clear/' It is clear, in any event, that he considers the system decimal. B. L. van der Waerden (Science Awakening, p. 41) says: "In a certain sense, the choice of 60 is a historical accident; 10, which appears everywhere (probably because we all have 10 fingers), is followed by 20 among the Celts (remember the French numerals quatre-vingt and quatre-vingt-dix, and the English three score for 60), by 100 among the Egyptians, perhaps by 50 among the Teutonic peoples, and by 60 among the Sumerians." W. Schmidt (Sprachfamilien und Sprachenkreise der Erde) in his examination of the number systems of the world, though he notes that Sumerian belongs to the Caucasian (Japhetic) family of languages, some branches of which (e.g., Basque) are vigesimal, nonetheless refers to Sumerian as a quinary-decimal system with some traces of vigesimal counting (see pp. 366, 376, and 71). On the contrary we are going to claim that Sumerian is a quinary-vigesimal system, with a trace of 10-counting. This vigesimal character has, indeed, been noticed before, namely by A. R. Nykl*; his paper thus to some extent serves the same purpose as ours, but we will make some additional observations.