  We call a finite group G ultrasolvable if it has a characteristic subgroup
series whose factors are cyclic. It was shown by Durbin--McDonald that the
automorphism group of an ultrasolvable group is supersolvable. The converse
statement was established by Baartmans--Woeppel under the hypothesis that G has
no direct factor isomorphic to the Klein four-group. We extend this result by
proving that Aut(G) is supersolvable if and only if G is ultrasolvable or
G=H\times C_2\times C_2 where H is ultrasolvable of odd order. This corrects an
erroneous claim by Corsi Tani. Our proof is more elementary than
Baartmans--Woeppel's and uses some ideas of Corsi Tani and Laue.
