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∈C^n, n≥2, where P(z) is a homogeneous polynomial of degree k with an isolated singularity at 0∈C^n and Milnor number μ. We prove that there exists a holomorphic change of coordinate ϕ such that ϕ(M)=(Re(h)=0) where h(z) is a polynomial of degree μ+1 and j^k_0(h)=P.