  We study pseudo-Riemanniasn manifolds $(M,g)$ with transitive group of
conformal transformation which is essential, i.e. does not preserves any metric
conformal to $g$. All such manifolds of Lorentz signature with non exact
isotropy representation of the stability subalgebra are described. A
construction of essential conformally homogeneous manifolds with exact isotropy
represenatation is given. Using spinor formalism, we prove that it provides all
4-dimensional non conformally flat Lorentzian 4-dimensional manifolds with
transitive essentially conformal group.
