  We study instability of a vortex soliton $e^{i(m\theta+\omega
t)}\phi_{\omega,m}(r)$ to $$iu_t+\Delta u+|u|^{p-1}u=0,\quad\text{for
$x\in\R^n$, $t>0$,}$$ where $n=2$, $m\in\N$ and $(r,\theta)$ are polar
coordinates in $\R^2$. Grillakis \cite{Gr} proved that every radially standing
wave solutions are unstable if $p>1+4/n$. However, we do not have any examples
of unstable standing wave solutions in the subcritical case $(p<1+n/4)$.
  Suppose $\phi_{\omega,m}$ is nonnegative. We investigate a limiting profile
of $\phi_{\omega,m}$ as $m\to\infty$ and prove that for every $p>1$, there
exists an $m_*\in \N$ such that for $m\ge m_*$, a vortex soliton
$e^{i(m\theta+\omega t)}\phi_{\omega,m}(r)$ becomes unstable to the
perturbations of the form $e^{i(m+j)\theta}v(r)$ with $1\ll j\ll m$.
