  We present the study of the decay $J/\psi \rightarrow \rho\pi$. The results
are based on of 5.2~million $J/\psi$ events collected by the KEDR detector at
the VEPP-4M collider. The branching fractions are measured to be $\B(J/\psi
\rightarrow \rho\pi) = \big(2.072\pm 0.017 \pm 0.062 \big)\cdot 10^{-2}$ and
$\B(J/\psi \rightarrow \pi^+\pi^-\pi^0) = \big(1.878 \pm 0.013 \pm 0.051
\big)\cdot 10^{-2}$, where the first uncertainties are statistical and the
second systematic. Our results are more precise than the previous relative
measurements.
