  Let $\Gamma^{(x_0)}$ be a finite rooted tree, for which $\Gamma$ is the
underlying tree and $x_0$ the root. Let $T$ be the Terwilliger algebra of
$\Gamma$ with respect to $x_0$. We study the structure of the principal
$T$-module. As a result, it is shown that $T$ recognizes the isomorphism class
of $\Gamma^{(x_0)}$.
