In Theorems 1 and 2 of [] necessary and sufficient conditions were given for a group G to have a finite automorphism group Aut G and a semisimple subgroup of central automorphisms AutcG. Recently it occurred to us, as a result of conversations with Ursula Webb, that these conditions could be stated in a much simpler and clearer form. Our purpose here is to record this reformulation. For an explanation ofterminology and notation we refer the reader to [1].