  In this paper, we prove that if
$R\colon\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ is a postcritically finite
rational map with Julia set homeomorphic to the Sierpi\'nski carpet, then there
is an integer $n_0$, such that, for any $n\ge n_0$, there exists an
$R^n$-invariant Jordan curve $\Gamma$ containing the postcritical set of $R$.
