  The CKM matrix elements $V_{cb}$ and $V_{ub}$ can be obtained by combining
data from the experiments with lattice QCD results for the semi-leptonic form
factors for the $\bar{B} \to D^\ast \ell \bar{\nu}$ and $\bar{B} \to \pi \ell
\bar{\nu}$ decays.
  It is highly desirable to use the Oktay-Kronfeld (OK) action for the form
factor calculation on the lattice, since the OK action is designed to reduce
the heavy quark discretization error down to the $\mathcal{O}(\lambda^4)$ level
in the power counting rules of the heavy quark effective theory (HQET).
  Here, we present a matching calculation to improve heavy-heavy and
heavy-light currents up to the $\lambda^3$ order in HQET, the same level of
improvement as the OK action. Our final results for the improved currents are
being used in a lattice QCD calculation of the semi-leptonic form factors for
the $\bar{B} \to D^\ast \ell \bar{\nu}$ and $\bar{B} \to D \ell \bar{\nu}$
decays.
