  We compute the fully differential decay rate of the Standard Model Higgs
boson into b-quarks at next-to-next-to-leading order (NNLO) accuracy in
alpha_S. We employ a general subtraction scheme developed for the calculation
of higher order perturbative corrections to QCD jet cross sections, which is
based on the universal infrared factorization properties of QCD squared matrix
elements. We show that the subtractions render the various contributions to the
NNLO correction finite. In particular, we demonstrate analytically that the sum
of integrated subtraction terms correctly reproduces the infrared poles of the
two-loop double virtual contribution to this process. We present illustrative
differential distributions obtained by implementing the method in a parton
level Monte Carlo program. The basic ingredients of our subtraction scheme,
used here for the first time to compute a physical observable, are universal
and can be employed for the computation of more involved processes.
