Let F(z) = Re(P(z)) + h.o.t be such that M = (F = 0) defines a germ of real analytic Levi-flat at 0 ∈ ℂn, n ≥ 2, where P (z) is a homogeneous polynomial of degree k with an isolated singularity at 0 ∈ ℂn and Milnor number μ. We prove that there exists a holomorphic change of coordinate φ{symbol} such that φ{symbol}(M) = (Re(h) = 0), where h(z) is a polynomial of degree μ + 1 and j0k(h)= P. © 2011 Springer.