F. Haimo and E. Schenkman [1] raised the question: Does a nilpotent group G always possess an outer automorphism? The answer is in the affirmative if G is finite and nilpotent of class 2, as is seen from a Schenkman's [I ] stronger result. The object of this note is to show that the answer is also in the affirmative for another family of nilpotent groups, namely the family of all finite p-groups G of order greater than 2 such that xi = e for every element x in G. Actually, our result is somewhat stronger: