Lattice calculations of the form factors for $\bar{B}\to D^{(*)}\ell\bar{\nu}$
decays can be used to extract the CKM matrix element $|V_{cb}|$.
The Oktay-Kronfeld action is a highly improved version of the Fermilab action,
which systematically reduces heavy quark discretization effects through
$\mathcal{O}(\lambda^3)$ in HQET power counting, for heavy-light meson
quantities.
To calculate $\bar{B}\rightarrow D^{(*)}\ell \bar{\nu}$ semi-leptonic
form factors using Oktay-Kronfeld heavy quarks, we need to improve the
heavy quark currents to the same level.
We report our progress in calculating the improvement coefficients
for currents composed of bottom and charm quarks.
Our results presented in this paper are preliminary.