  This paper discusses the possibility to observe a signal from MSSM Higgs
boson decays into final states containing four b-jets. Two specific channels
are considered: bbH and bbA production with H,A -->bb, for large values of mH,
mA and tan(beta), and H-->hh-->bbbb decays for 150 GeV < mH < 2 and for low
values of tan(beta). Both channels are difficult to extract because of the very
large reducible and irreducible QCD backgrounds. Even with an ultimate
integrated luminosity, expected per LHC experiment, of 3*10**5 pb**-1, the
region of the MSSM parameter space covered by these channels does not extend
the reach beyond that accessible to other channels that were studied in the
past. Nevertheless, their observation would help in constraining the couplings
and branching ratios of the MSSM Higgs bosons.
