  Based on a sample of 1.31 billion $J/\psi$ events collected with the BESIII
detector, we perform a search for the rare decay $\eta'\rightarrow 4\pi^{0}$
via $J/\psi\rightarrow\gamma\eta'$. No significant $\eta'$ signal is observed
in the invariant mass spectrum of 4$\pi^{0}$. With a Bayesian approach, the
upper limit on the branching fraction of $\eta'\rightarrow 4\pi^{0}$ is
determined to be $\mathcal{B}(\eta'\rightarrow 4\pi^{0})$ $< 4.94\times10^{-5}$
at the 90\% confidence level, which is a factor of six smaller than the
previous experimental limit.
