  Let $a$ be a real euclidean vector space of finite dimension and $\Sigma$ a
root system in $a$ with a basis $\Delta$. Let $\Theta \subset \Delta$ and $M =
M_{\Theta}$ be a standard Levi of a reductive group $G$ such that $a_\Theta =
a_M / a_G$. Let us denote $d$ the dimension of $a_\Theta$, i.e the cardinal of
$\Delta - \Theta$ and $\Sigma_{\Theta}$ the set of all non-trivial projections
of roots in $\Sigma$. We obtain conditions on $\Theta$ such that
$\Sigma_\Theta$ contains a root system of rank $d$.
