For the m-valued (2<w<∞) logics of Łukasiewicz as described in [2] using the values 1,2, …, m and based on the functions f(p, q) = max(1,q—p+1) and g(p) = m—p+1, Evans and Schwartz have essentially2 proved in [1] that the addition of a constant function i, 1<i<m, yields functional completeness if and only if (m—1, i—1)= 1.3 In this note it will be shown that if n constant functions i1, …, in, 1<ik<m and 1≦k≦n, are added, functional completeness obtains if and only if (m—1, i1—1, …, in—1) = 1.