  We study relativistic corrections to exclusive $S$-wave charmonium decays
into $\rho\pi$ and $\gamma\pi$ final states. The contribution of relative order
$v^2$ and the set of associated higher order corrections are calculated using
NRQCD and collinear factorisation framework. Numerical estimates show that the
dominant effect is provided by the corrections of relative order $v^2$. The
numerical values of these contributions are of the same order as the
leading-order ones. These results suggest a scenario where the sum of
relativistic and radiative QCD corrections could explain the $\rho\pi$-puzzle.
