  We demonstrate that detection of the heavier minimal supersymmetric model
CP-even Higgs boson $H^0$ will be possible at the LHC via its $H^0\to h^0h^0\to
4b$ and/or $H^0\to A^0A^0\to 4b$ decay channels for significant portions of the
$( m_{A^0},\tan\beta)$ model parameter space. At low $ m_{A^0}$ ($\lsim
60\gev$), {\it both} the $H^0\to A^0A^0\to 4b$ and $H^0\to h^0h^0\to 4b$ modes
yield a viable signal for most $\tan\beta$ values; viability for the $h^0h^0$
channel extends up to $\mhh\sim 2\mt$ when the model parameter $\tan\beta$ is
not large. At the Tevatron, the $h^0h^0$ and $A^0A^0$ channels are both
potentially viable at low $ m_{A^0}$ for sufficiently good $b$-tagging
efficiency and purity.
