Let \(q\) be a power of a prime \(p\), let \(G\) be a finite Chevalley group over \(\mathbb{F}_q\) and let \(U\) be a Sylow \(p\)-subgroup of \(G\); we assume that \(p\) is not a very bad prime for \(G\). We explain a procedure of reduction of irreducible complex characters of \(U\), which leads to an algorithm whose goal is to obtain a parametrization of the irreducible characters of \(U\) along with a means to construct these characters as induced characters. A focus in this paper is determining the parametrization when \(G\) is of type \(\mathrm{F}_4\), where we observe that the parametrization is "uniform" over good primes \(p > 3\), but differs for the bad prime \(p = 3\). We also explain how it has been applied for all groups of rank \(4\) or less.