  Radiative corrections to both perturbative and non-perturbative contributions
are added to existing calculations of the Isgur-Wise function $\xi_{IW}$. To
this end, we develop a method for calculating two-loop integrals in the heavy
quark effective theory involving two different scales. The inclusion of
$O(\alpha_s)$ terms causes $\xi_{IW}$ to decrease as compared to the lowest
order result and shows the importance of quantum effects. The slope parameter
$\rho^2$ violates the bound given by de Rafael and Taron.
