  We reinvestigated the parameter space allowing a large BR of the 4-body decay
of the lighter top-squark ($\lstop$) accessible at Tevatron Run-II by imposing
the lighter CP-even Higgs boson mass ($\mlhiggs$) bound from LEP. Important
constraints were obtained in mSUGRA as well as in the unconstrained
supersymmetric models. Our results show that the prospect of searching the
lighter top-squark via the 4-body decay mode, in particular the $\ell + n-jets
+ \met$ signal, is not promising in mSUGRA due to the above bound on
$\mlhiggs$. The existing bounds on $\mlstop$ from Tevatron Run-I and LEP
assuming 100% BR of the loop decay of $\lstop$ are, therefore, valid to a good
approximation. We also find that large BRs of the above 4-body decay are
allowed in the unconstrained model over significant regions of parameter spaces
and the possibility that this decay mode is the main discovery channel at
Tevatron Run-II is open. We have briefly reviewed the theoretical uncertainties
in the calculation of $\mlhiggs$ and their consequences for the constraints
obtained by us. We have commented upon, with illustrative examples, how the
above parameter space is affected if future experiments push the Higgs boson
mass bound upward.
