  We perturbatively determine O($a$) boundary improvement coefficients at
1-loop for the Schr\"odinger Functional coupling with improved gauge actions.
These coefficients are required to implement the 1-loop O($a$) improvement in
full QCD simulations for the coupling with the improved gauge actions. To this
order, lattice artifacts of the step scaling function (SSF) for each improved
gauge action are also investigated. Furthermore, we investigate the effect of
the 1-loop O($a$) improvement to the SSF in numerical simulations of the pure
SU(3) gauge theory.
