  Upper bounds for neutral as well as charged Higgs boson masses in a
two-doublet model are obtained on the basis of tree unitarity conditions \`a la
Lee, Quigg and Thacker. A wide variety of scattering processes are considered
so extensively that our bounds are more restrictive than those obtained
previously for neutral Higgs bosons and are also of a new kind for charged
Higgs boson. It is argued that at least one of the Higgs bosons should be
lighter than 580 ${\rm GeV}/c^{2}$.
