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.
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