  We develop in this work a method to parametrize the set $\mathrm{Irr}(U)$ of
irreducible characters of a Sylow $p$-subgroup $U$ of a finite Chevalley group
$G(p^f)$ which is valid for arbitrary primes $p$, in particular when $p$ is a
very bad prime for $G$. As an application, we parametrize $\mathrm{Irr}(U)$
when $G=\mathrm{F}_4(2^f)$.
