  We prove that for any operator $T$ on bi--parameter BMO the identity factors
through $T$ or $I - T$. Bourgain's localization method provides the conceptual
framework of our proof. It consists in replacing the factorization problem on
the non--separable bi--parameter BMO by its localized, finite dimensional
counterpart. We solve the resulting finite dimensional factorization problems
by exploiting the geometry and combinatorics of colored dyadic rectangles.
