Algebraicity of real analytic hypersurfaces with maximal rank

Let M be a connected strongly pseudoconvex real analytic hypersurface in Cⁿ⁺¹. Suppose that (M, p) is of maximal rank for any p ∈ M. It is shown that the following two statements are equivalent: (i) There exists a certain point p₀ ∈ M such that (M, p₀) is CR isomorphic to a germ of a real algebraic hypersurface. (ii) For any point p ∈ M, (M, p) is CR isomorphic to a germ of a real algebraic hypersurface.