  Unitarity constraints on the scalar parameters both for the Standard Model
and the general Two Higgs Doublet Model (THDM) are examined. In the case of the
THDM with an exact discrete symmetry transformation, we show that the mass of
the lightest CP-even Higgs boson ($M_h$) and $\tan\beta$ are strongly
correlated and consequently a strong lower bound can be put on $M_h$ for large
$\tan\beta$. It is also shown that the inclusion of the discrete symmetry
breaking term relaxes the aforementioned correlation.
