We study the localization of the interior transmission eigenvalues (ITEs) in the case when the domain is the unit ball $\{x ∈ \mathbb{R}^d:\: |x| ≤ 1\}, \: d≥ 2,$ and the coefficients $c_j(x), \: j =1,2, $ and the indices of refraction $n_j(x), \: j =1,2,$ are constants near the boundary $|x| = 1$ . We prove that in this case the eigenvalue-free region obtained in [
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