  If a fourth generation quark exists whose mass is below 255 GeV, then the
only two-body charged current decay, b'-->cW, is doubly-Cabibbo suppressed. For
this reason, CDF has searched for the one-loop neutral current decay b' --> bZ,
assuming that the branching ratio into bZ is 100%; an analysis giving the
bounds on m_b' for smaller branching ratios is in preparation. In this Report,
we examine the neutral current decay b' --> bH, which will occur if the Higgs
mass is less than m_b'-m_b. Four different cases are examined: the sequential
case, the non-chiral isosinglet case, the non-chiral isodoublet case, and a
two-Higgs model with flavor-changing neutral currents. In the first three of
these, the rates for b' --> bZ and b' --> bH are comparable, assuming
comparable phase space factors; in the fourth, b' --> bH is completely
dominant. Thus, we emphasize the importance of giving b' mass bounds as a
function of the branching ratio into bZ, since the assumption of a 100%
branching ratio for b' --> bZ may only be valid if the Higgs mass is near or
above the b' mass.
