  Let $q$ be a prime power and $F_4(q)$ be the Chevalley group of type $F_4$
over a finite field with $q$ elements. Marcelo--Shinoda (1995) determined the
values of the unipotent characters of $F_4(q)$ on all unipotent elements,
extending earlier work by Kawanaka and Lusztig to small characteristics.
Assuming that $q$ is a power of~$2$, we explain how to construct the complete
character table of~$F_4(q)$.
