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 VEPP-4M collider. The branching fraction is measured to be \(\mathcal{B}(J/\psi\rightarrow\rho\pi) = \big(2.072\pm 0.017 \pm 0.056 \big)\cdot 10^{-2}\) where the first uncertainty is statistical, the second one is systematic. This is the most precise single measurement of this quantity at the moment.