We extend the resolution of
the CR Yamabe conjecture for one of the two cases left open by D. Jerison and J.M.
Lee: The CR locally conformally flat case.
The proof is based on techniques related to the theory of critical points
at infinity. These techniques were first introduced by A. Bahri, A. Bahri
and H. Brezis for the resolution of the same conjecture for the Riemannian
case.