  We perform a numerical test of a relativistic heavy quark(RHQ) action,
recently proposed by Tsukuba group, in quenched lattice QCD at $a\simeq 0.1$
fm. With the use of the improvement parameters previously determined at
one-loop level for the RHQ action, we investigate a restoration of rotational
symmetry for heavy-heavy and heavy-light meson systems around the charm quark
mass. We focused on two quantities, the meson dispersion relation and the
pseudo-scalar meson decay constants. It is shown that the RHQ action
significantly reduces the discretization errors due to the charm quark mass. We
also calculate the S-state hyperfine splittings for the charmonium and
charmed-strange mesons and the $D_s$ meson decay constant. The remaining
discretization errors in the physical quantities are discussed.
