We analyze the univalence of the solutions of the biharmonic equation. In particular, we show that if F is a biharmonic map in the form F(z) = r 2 G(z), |z| < 1, where G is harmonic, then F is starlike whenever G is starlike. In addition, when F(z) = r 2 G(z) + K(z), |z| < 1, where G and K are harmonic, we show that F is locally univalent whenever G is starlike and K is orientation preserving. (1.4)