  We evaluate the complete four-loop anomalous dimension matrix that is
necessary for determining the effective flavour-changing neutral current
couplings qbar-q'-gamma and qbar-q'-g at the next-to-next-to-leading order in
QCD. The resulting O(alpha_s^2(mu_b)) correction to the B -> X_s gamma
branching ratio amounts to around -2.9% for mu_b = 5 GeV, and -4.4% for mu_b =
2.5 GeV
