  We prove that the automorphism group of an arbitrary non-abelian free group
is complete. It generalizes the result by J.Dyer and E.Formanek (1975) stating
the completeness of automorphism group of finitely generated free groups. Using
the description of involutions in automorphism groups of free groups (J. Dyer,
P. Scott, 1975) we obtain a group-theoretic characterization of inner
automorphisms determined by primitive elements in the automorphism group of any
non-abelian free group F. It follows that the subgroup Inn(F) is characteristic
in Aut(F), and hence the latter one is complete.
