  We consider a generalized Schr\"odinger operator in $L^2(\mathbb R^2)$
describing an attractive $\delta'$ interaction in a strong coupling limit.
$\delta'$ interaction is characterized by a coupling parameter $\beta$ and it
is supported by a $C^4$-smooth infinite asymptotically straight curve $\Gamma$
without self-intersections. It is shown that in the strong coupling limit,
$\beta\to 0_+$, the eigenvalues for a non-straight curve behave as
$-\frac{4}{\beta^2} +\mu_j+\mathcal O(\beta|\ln\beta|)$, where $\mu_j$ is the
$j$-th eigenvalue of the Schr\"odinger operator on $L^2(\mathbb R)$ with the
potential $-\frac14 \gamma^2$ where $\gamma$ is the signed curvature of
$\Gamma$.
