  Let $G$ be a reductive $p$-adic group. We give a short proof of the fact that
$G$ always admits supercuspidal complex representations. This result has
already been established by A. Kret using the Deligne-Lusztig theory of
representations of finite groups of Lie type. Our argument is of a different
nature and is self-contained. It is based on the Harish-Chandra theory of cusp
forms and it ultimately relies on the existence of elliptic maximal tori in
$G$.
