  Non-$D\bar{D}$ decay $\psppto \rhopi$ is searched for using a data sample of
$(17.3\pm 0.5) pb^{-1}$ taken at the center-of-mass energy of 3.773 GeV by the
BESII detector at the BEPC. No $\rhopi$ signal is observed, and the upper limit
of the cross section is measured to be $\sigma(\EETO \rhopi)<6.0 pb$ at 90% C.
L. Considering the interference between the continuum amplitude and the $\pspp$
resonance amplitude, the branching fraction of $\pspp$ decays to $\rho\pi$ is
determined to be $\BR(\pspp\ra\rho\pi)\in(6.0\times10^{-6}, 2.4\times10^{-3})$
at 90% C. L. This is in agreement with the prediction of the $S$- and $D$-wave
mixing scheme of the charmonium states for solving the ``$\rhopi$ puzzle''
between $\jpsi$ and $\psp$ decays.
