  We construct discontinuous point of the Lyapunov exponent of quasiperiodic
Schr\"odinger cocycles in the Gevrey space $G^{s}$ with $s>2$. In contrast, the
Lyapunov exponent has been proved to be continuous in the Gevrey space $G^{s}$
with $s<2$ \cite{klein,cgyz}. This shows that $G^2$ is the transition space for
the continuity of the Lyapunov exponent.
