  We elucidate the relation between the restricted Weyl symmetry and
spontaneous symmetry breakdown of conformal symmetry. Using a scalar-tensor
gravity, we show that the restricted Weyl symmetry leads to spontaneous
symmetry breakdown of a global scale symmetry when the vacuum expectation value
of a scalar field takes a non-zero value. It is then shown that this
spontaneous symmetry breakdown induces spontaneous symmetry breakdown of
special conformal symmetry in a flat Minkowski space-time, but the resultant
Nambu-Goldstone boson is not an independent physical mode but expressed in
terms of the derivative of the dilaton which is the Nambu-Goldstone boson of
the global scale symmetry. In other words, the theories which are invariant
under the general coordinate transformation and the restricted Weyl
transformation exhibit a Nambu-Goldstone phase where both special conformal
transformation and dilatation are spontaneously broken while preserving the
Poincar\'{e} symmetry.
