let $x=(x_t)_{t\ge 0}$ be a self-similar markov process with values in the non-negative half line, such that the state $0$ is a trap. we present a necessary and sufficient condition for the existence of a self-similar recurrent extension of $x$ that leaves $0$ continuously. this condition is expressed in terms of the l\'evy process associated with $x$ by the lamperti transformation.