  The number of diagrams of stationary points free vector fields in the 2-disk
$\mathbb{B}^{2}$ is counted in the article. It is shown that the number of such
diagrams with $2k$ exceptional points on the boundary $\mathbb{S}^{1}$ equals
$3^{k-2}(C_{k}+2C_{k-1})$, where $C_{k}$ is the corresponding Catalan number.
An algorithm for finding all such diagrams is discussed.
