The Szegö kernel $S(z,\zeta)$ on the boundary of
strictly pseudoconvex domains has been studied extensively. We
can consider model domains $\Omega = \{ (z_1,z_2) \in
\mathbb{C}^2 \mid -\Im z_2 > b(\Re z_1)\}$. If $b$ is convex,
one has $|S(z,\zeta)| \le c|B(z,\delta)|^{-1}$, where
$B(z,\delta)$ is the nonisotropic ball with center $z$ and
radius $\delta$, and $\delta $ is the nonisotropic distance
from $z$ to $\zeta$. The only singularities are on the
diagonal $z=\zeta$. In this paper, we obtain estimates for
$|S|$ when the function $b$ is a certain non-convex
function. We show that near certain points, there are
singularities off the diagonal.