A common statement in papers in the vectorization field is to note that point SOR methods with the natural ordering cannot be vectorized. The usual approach is to re-order the unknowns using a red-black or diagonal ordering and vectorize that. In this paper, we construct a point Gauss-Seidel iteration which completely vectorizes and still uses the natural ordering. The work here also applies to point SOR. When this approach is reasonable to use is also shown.