  We compute the O(ab*as) two-loop corrections to the neutral Higgs boson
masses in the Minimal Supersymmetric Standard Model, using the effective
potential approach. Such corrections can be important in the region of
parameter space corresponding to tan(beta)>>1 and sizeable mu. In spite of the
formal analogy with the O(at*as) corrections, there are important differences,
since the dominant effects are controlled by the sbottom-Higgs scalar
couplings. We propose a convenient renormalization scheme that avoids
unphysically large threshold effects associated with the bottom mass, and
absorbs the bulk of the O(ab*as + ab*at) corrections into the one-loop
expression. We give general explicit formulae for the O(ab*as) corrections to
the neutral Higgs boson mass matrix. We also discuss the importance of the
O(ab^2) corrections and derive a formula for their contribution to mh in a
simple limiting case.
