  We report measurement of the cross section of $e^+e^-\to \pi^+\pi^-\psi(2S)$
between 4.0 and $5.5 {\rm GeV}$, based on an analysis of initial state
radiation events in a $980 \rm fb^{-1}$ data sample recorded with the Belle
detector. The properties of the $Y(4360)$ and $Y(4660)$ states are determined.
Fitting the mass spectrum of $\pi^+\pi^-\psi(2S)$ with two coherent
Breit-Wigner functions, we find two solutions with identical mass and width but
different couplings to electron-positron pairs: $M_{Y(4360)} = (4347\pm 6\pm 3)
{\rm MeV}/c^2$, $\Gamma_{Y(4360)} = (103\pm 9\pm 5) {\rm MeV}$, $M_{Y(4660)} =
(4652\pm10\pm 8) {\rm MeV}/c^2$, $\Gamma_{Y(4660)} = (68\pm 11\pm 1) \rm MeV$;
and ${\cal{B}}[Y(4360)\to \pi^+\pi^-\psi(2S)]\cdot \Gamma_{Y(4360)}^{e^+e^-} =
(10.9\pm 0.6\pm 0.7) \rm eV$ and ${\cal{B}}[Y(4660)\to \pi^+\pi^-\psi(2S)]\cdot
\Gamma_{Y(4660)}^{e^+e^-} = (8.1\pm 1.1\pm 0.5) \rm eV$ for one solution; or
${\cal{B}}[Y(4360)\to \pi^+\pi^-\psi(2S)]\cdot \Gamma_{Y(4360)}^{e^+e^-} =
(9.2\pm 0.6\pm 0.6) \rm eV$ and ${\cal{B}}[Y(4660)\to \pi^+\pi^-\psi(2S)]\cdot
\Gamma_{Y(4660)}^{e^+e^-} = (2.0\pm 0.3\pm 0.2) \rm eV$ for the other. Here,
the first errors are statistical and the second systematic. Evidence for a
charged charmoniumlike structure at $4.05 {\rm GeV}/c^2$ is observed in the
$\pi^{\pm}\psi(2S)$ intermediate state in the $Y(4360)$ decays.
