  Motivated by the issue of whether it is possible to construct
phenomenologically viable models where the electroweak symmetry breaking is
triggered by new physics at a scale $\Lambda \gg 4\pi v$, where $v$ is the
order parameter of the transition ($v\sim 250$ GeV) and $\Lambda$ is the scale
of new physics, we have studied the phase diagram of the $U(2) \times U(2)$
model. This is the relevant low energy effective theory for a class of models
which will be discussed below. We find that the phase transition in these
models is first order in most of parameter space. The order parameter can not
be made much smaller than the cut-off and, consequently a large hierarchy does
not appear sustainable. In the relatively small region in the space of
parameters where the phase transition is very weakly first order or second
order the model effectively reduces to the O(8) theory for which the triviality
considerations should apply.
