  We investigate the constraints on flavour-changing neutral heavy Higgs-boson
decays H-> b \bar s from b -> s gamma bounds on the flavour-mixing parameters
of the MSSM with non-minimal flavour violation (NMFV). In our analysis we
include the contributions from the SM and new physics due to general flavour
mixing in the squark mass matrices. We study the case of one and two non-zero
flavour-mixing parameters and find that in the latter case the interference can
raise the Higgs flavour-changing branching ratios by one or two orders of
magnitude with respect to previous predictions based on a single non-zero
parameter and in agreement with present constraints from $B$ physics. In the
course of our work we developed a new "FeynArts" model file for the NMFV MSSM
and added the necessary code for the evaluation to "FormCalc". Both extensions
are publicly available.
