  Preliminary results are presented in a step scaling determination of the
coefficients in the relativistic heavy quark action. By matching finite volume,
heavy-heavy and heavy-light meson masses, we attempt to determine the four
parameters ($m$, $\zeta$, $c_B$ and $c_E$) in the on-shell-improved, heavy
quark action. In this report we carry out one step in this program by matching
two physically equivalent systems. The first is a fully relativistic
calculation using a $24^3\times 48$, $1/a=5.4$ GeV lattice with both the heavy
and light quarks treated as domain wall fermions. The second calculation uses
at $16^3\times 32$, $1/a=3.6$ GeV lattice, a domain-wall light quark and a
heavy quark computed with the relativistic heavy quark action. The four
parameters in this heavy quark effective action are then varied to reproduce
the mass spectrum from the first calculation. These calculations are carried
out in the quenched approximation for a heavy quark mass approximately that of
the charmed quark.
