  We present the O(alphas^4) virtual QCD corrections to gluon-gluon scattering
due to the self-interference of the one-loop amplitude. We give analytic
expressions renormalised in the MSbar scheme and work in conventional
dimensional regularisation. We write the structure of the infrared divergences
from direct Feynman diagram evaluation in terms of the Catani formalism for
infrared divergences. Formulae for the finite remainder are given in terms of
logarithms that are real in the physical region. These results, together with
those previously obtained for quark-quark and quark-gluon scattering complete
the one-loop matrix elements for 2 to 2 processes needed for the
next-to-next-to-leading order contribution to inclusive jet production at
hadron colliders.
