  We obtain a kind of structure theorem for the automorphism group ${\rm
Aut}{\cal A}$ of a unital C$^{*}$-algebra ${\cal A}$. According to it, ${\rm
Aut}{\cal A}$ can be regarded as a subgroup of the semi-direct product of
direct product group consisting of some family of projective unitary groups and
some permutation group on the spectrum of ${\cal A}$.
