  The Two Higgs Doublet Model invariant under the gauge group SU(2)xU(1) is
known to have six additional global discrete or continuous symmetries of its
scalar sector. We have discovered regions of parameter space of the model which
are basis and renormalization group invariant to all orders of perturbation
theory in the scalar and gauge sectors, but correspond to none of the hitherto
considered symmetries. We therefore identify seven new symmetries of the model
and discuss their phenomenology. Soft symmetry breaking is required for some of
these models so that electroweak symmetry breaking can occur. We show that, at
least at the two-loop level, it is possible to extend some of these symmetries
to include fermions.
