In the joint work with X. Huang, a monotonicity property has been detected for a CR embedding from a Levi non-degenerate hypersurface into another one with the same signature. Roughly speaking, the CR embedding decreases the Chern-Moser-Weyl curvature along the null space of the Levi-form. The criterion allows us to construct many algebraic Levi non-degenerate hypersurfaces non-embeddable into hyperquadrics of the same signature.