  Denote by $\mathbb G(k,n)$ the Grassmannian of linear subspaces of dimension
$k$ in $\mathbb P^n$. We show that, if $\varphi:\mathbb G(l,n) \to \mathbb
G(k,n)$ is a non constant morphism and $l \not=0,n-1$ then $l=k$ or $l=n-k-1$
and $\varphi$ is an isomorphism.
