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Improved branching ratios were measured for the $K_L \to 3 \pi^0 $ decay in aneutral beam at the CERN SPS with the NA31 detector: $\Gamma (K_L \to 3 \pi^0)/ \Gamma (K_L \to \pi^+ \pi^- \pi^0) = 1.611 \pm 0.037$ and $\Gamma (K_L \to 3\pi^0) / \Gamma (K_L \to \pi e \nu ) = 0.545 \pm 0.010$.  From the first number an upper limit for $\Delta I =5/2$ and $\Delta I = 7/2$ transitions in neutral kaon decay is derived. Using older results for theKe3/K$\mu $3 fraction, the 3$\pi^0$ branching ratio is found to be $\Gamma (K_L\to 3 \pi^0 )/ \Gamma_{tot} = (0.211 \pm 0.003)$, about a factor three moreprecise than from previous experiments

Determination of the branching ratiosΓ(K L→3π0)/Γ(K L→π+ - 0) andΓ(K L→3π0)/Γ(K L→πev)