  In this article we prove that all completely multiplicative automatic
sequences $(a_n)_{n \in \mathbf{N}}$ defined on $\mathbf{C}$, vanishing or not,
can be written in the form $a_n=b_n\chi_n$ where $(b_n)_{n \in \mathbf{N}}$ is
an almost constant sequence, and $(\chi_n)_{n \in \mathbf{N}}$ is a Dirichlet
character.
