In this note is proved the following:Theorem.Iƒ A × B is universal and one oƒ A, B is r.e. then one of A, B is universal.Letα, τbe 1-argument recursive functions such thatxgoes to, τ) is a map of the natural numbers onto all ordered pairs of natural numbers. A set A of natural numbers is calleduniversalif every r.e. set is reducible to A; A × B is calleduniversalif the set.