We present in analytic form the O(alpha_s^5) correction to the H→gg
partial width of the standard-model Higgs boson with intermediate mass
M_H<2M_t. Its knowledge is useful because the O(alpha_s^4) correction
is sizeable (around 20%). For M_H=120 GeV, the resulting QCD
correction factor reads
1 + (215/12) alpha_s^(5)(M_H)/pi
+ 152.5 (alpha_s^(5)(M_H)/pi)^2
+ 381.5 (alpha_s^(5)(M_H)/pi)^3
\approx 1+0.65+0.20+0.02.
The new four-loop correction increases the total Higgs-boson hadronic
width by a small amount of order 1 promille and stabilizes
significantly the residual scale dependence.
