  A search for rare decay $\eta' \rightarrow 4 \pi^{0}$ has been performed with
GAMS-4$\pi$ Setup. The new upper limit for decay was established $BR(\eta'
\rightarrow 4 \pi^{0}) < 3.2 \cdot 10^{-4}$ at 90\% confidence level. The
$\pi^{-} p$ charge-exchange reaction at 32.5 GeV/c was used as a source of
$1.3\cdot 10^{6}$ $ \eta'$ mesons. Experiment carried out at the IHEP U-70
accelerator.
