  We explicitly determine all Rota-Baxter operators (of weight zero) on
$sl(2,C)$ under the Cartan-Weyl basis. For the skew-symmetric operators, we
give the corresponding skew-symmetric solutions of the classical Yang-Baxter
equation in $sl(2,C)$, confirming the related study by Semenov-Tian-Shansky. In
general, these Rota-Baxter operators give a family of solutions of the
classical Yang-Baxter equation in the 6-dimensional Lie algebra $sl(2,C)
\ltimes_{{\rm ad}^{\ast}} sl(2,C)^{\ast}$. They also give rise to 3-dimensional
pre-Lie algebras which in turn yield solutions of the classical Yang-Baxter
equation in other 6-dimensional Lie algebras.
