  In the framework of the Constrained Minimal Supersymmetric Standard Model
(CMSSM) we discuss the impact of the recent experimental information,
especially from E821 Brookhaven experiment on $g_{\mu}-2$ along with the light
Higgs boson mass bound from LEP, to the Dark Matter direct searches. Imposing
these experimental bounds, the maximum value of the spin-independent
neutralino-nucleon cross section turns out to be of the order of $10^{-8}$ pb
for large values of $\tan\beta$ and low $M_{1/2}, m_0$. The effect of the
recent experimental bounds is to decrease the maximum value of the cross
section by about an order of magnitude, demanding the analogous sensitivity
from the direct Dark Matter detection experiments.
