  The partial Higgs width $\Gamma (H \longrightarrow \gamma \gamma)$ is
important at the LHC for Higgs masses in the MSSM mass window up to 140 GeV as
a relatively background free signal of a fundamental scalar. At the photon
photon mode at the NLC it would be the Higgs production mechanism . Two loop
QCD corrections exist for the fermionic contribution and in the case of the
bottom loop large non-Sudakov double logarithms can be resummed to all orders
and contribute up to 12 % compared to the t-quark. In more complicated Higgs
sectors, such as in the MSSM, large $\tan \beta$ enhancements of bottom type
Yukawa couplings can potentially dominate even the whole partial width. A main
uncertainty in all existing calculations is the scale of the strong coupling as
it is only renormalized at the three loop level. In this paper we include the
exact two loop running coupling to all orders into the bottom contribution. We
find that the effective scale is close to $\alpha_s (10 m_b^2)$.
