  In this paper we discuss a model in which the energy density, corresponding
to the effective cosmological constant, after the $SU(2)\times U(1)$ symmetry
breaking appears to be of the desired order of $10^{-48}\div 10^{-47} GeV^{4}$.
The model contain two different energy scales, one of which is associated with
the Higgs's vacuum expectation value. Another scale is of the order of
$10^{21}GeV$ and defines the vacuum expectation value of the Brans-Dicke scalar
field, non-minimally coupled to gravity, and sets the value of the Planck mass.
Other (dimensionless) parameters are assumed not to contain hierarchical
differences. The model is devoid of any fine-tuning and gives a small value of
the effective cosmological constant even if the real "bare" cosmological
constant is quite large.
