  In this paper we consider an interval $[\theta_{1}, \theta_{2}] \subset [0,
\pi]$ and $f$ a differentiable, periodic and even function sufficiently smooth
such that $f(\theta) \in [f(\theta_{1}, f(\theta_{2})] \iff \theta \in
[\theta_{1}, \theta_{2}]$. Then we obtain an higher order asymptotic formula
for all the eigenvalues of the Toeplitz matrix $T_N(f)$ which belong to
$[f(\theta_{1}, f(\theta_{2})]$. Also given are three consequences for Toeplitz
matrices with trigonometric symbol.
