  Very recently a new enhancement around 4.05 GeV was observed by Belle
experiment. In this short note, we discuss some possible assignments for this
enhancement, i.e. $\psi(3S)$ and $D^*\bar{D}^*$ molecular state. In these two
assignments, Y(4008) can decay into $J/\psi\pi^0\pi^0$ with comparable
branching ratio with that of $Y(4008)\to J/\psi\pi^+\pi^-$. Thus one suggests
high energy experimentalists to look for Y(4008) in $J/\psi\pi^0\pi^0$ channel.
Furthermore one proposes further experiments to search missing channel
$D\bar{D}$, $D\bar{D}^*+h.c.$ and especially $\chi_{cJ}\pi^+\pi^-\pi^0$ and
$\eta_c\pi^+\pi^-\pi^0$, which will be helpful to distinguish $\psi(3S)$ and
$D^*\bar{D}^*$ molecular state assignments for this new enhancement.
