Abstract. We prove stability of the kink solution of the Cahn-Hilliard equation $\partial_t u = \partial_x^2 \bigl( - \partial_x^2 u - u /2 + u^3 / 2 \bigr),$ $x \in {\BbbR}$. The proof is based on an inductive Renormalization Group method and we obtain detailed asymptotics of the solution as $t\to\infty$.