  We develop an improved lattice action for heavy quarks based on
Brillouin-type fermions, that have excellent energy-momentum dispersion
relation. The leading discretization errors of $O(a)$ and $O(a^2)$ are
eliminated at tree-level. We carry out a scaling study of this improved
Brillouin fermion action on quenched lattices by calculating the charmonium
energy-momentum dispersion relation and hyperfine splitting. We present a
comparison to standard Wilson fermions and domain-wall fermions.
