  For the complex interior transmission eigenvalues (ITE) we study for small
$\theta > 0$ the counting function $$N(\theta, r) = #\{\lambda \in \C:\:
\lambda \: {\rm is} \: {\rm (ITE)},\: |\lambda| \leq r, \: 0 \leq \arg \lambda
\leq \theta\}.$$ We obtain for fixed $\theta > 0$ an upper bound $N(\theta, r)
\leq C r^{n/2}, \: r \geq r(\theta).$
