  We investigate the general two Higgs doublet model imposing both the
unitarity conditions and the bounded-from-below conditions. Both types of
conditions restrict the ranges of the parameters of the scalar potential. We
study the model in the Higgs basis, i.e. in the basis for the scalar doublets
where only one doublet has vacuum expectation value. We use the experimental
bounds on the oblique parameter T, to produce scalar particles with masses and
cubic and quartic couplings of the Higgs in agreement with the phenomenology.
The numerical calculations show that the cubic coupling may be up to 1.6 times
larger than in the Standard Model, but it may also be zero or even negative.
The quartic coupling is always positive and may be up to four times larger than
in the Standard Model.
