Using a sample of 1.31 x 10(9) J/psi events collected with the BESIII detector, we perform a search for the rare decay if eta' -> 4 pi(0) via J/psi -> gamma eta'. No significant eta' signal is observed in the 4 pi(0) invariant mass spectrum. With a Bayesian approach, the upper limit on the branching fraction is determined to be B(eta' -> 4 pi(0)) < 4.94 x 10(-5) at the 90% confidence level, which is a factor of 6 smaller than the previous experimental limit.
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