  A cluster automorphism is a $\mathbb{Z}$-algebra automorphism of a cluster
algebra $\mathcal A$ satisfying that it sends a cluster to another and commutes
with mutations. Chang and Schiffler conjectured that a cluster automorphism of
$\mathcal A$ is just a $\mathbb{Z}$-algebra homomorphism of a cluster algebra
sending a cluster to another. The aim of this article is to prove this
conjecture.
