We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 . The first class is formed by the polynomials maps of the form (q(x)-p(y), q(y)+p(x)) : R 2 ⟶ R 2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by polynomials maps (f, g): R 2 ⟶ R 2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions.