  We study the gravity action built from two gauge fields corresponding to the
generators of the conformal group. Starting with the action from which one can
obtain Einstein gravity and conformal gravity upon imposing suitable
constraints, we keep two independent gauge fields and integrate out the field
corresponding to the generator of Lorentz transformations. We identify the two
gauge fields with two vierbeins and perturb them around an Anti--de Sitter
space. This gives the linearized equations that differ from both, Einstein
gravity and conformal gravity linearized equations. We also study the
linearized equations for one gauge field perturbed around the flat space and
one around zero, and the case when the gauge fields are proportional to each
other.
