  Let $L$ be a restricted Cartan type Lie algebra over an algebraically closed
field $k$ of characteristic $p>3$, and let $G$ denote the automorphism group of
$L$. We prove that there are no nontrivial invariants of $L^*$ under the
coadjoint action of $G$, i.e., $k[L^*]^G=k$. This property characterises the
Cartan type algebras among the restricted simple Lie algebras.
