  We present a new search for the $K_S \to 3\pi^0$ decay performed with the
KLOE detector operating at the DA$\Phi$NE $\phi$--factory. The $K_S$ mesons
were tagged via registration of $K_L$ mesons which crossed the drift chamber
without decaying and interacted with the KLOE electromagnetic calorimeter. The
$K_S \to 3\pi^0$ decay was then searched requiring six prompt photons. To
suppress background, originating from fake $K_S$ tags and $K_S \to 2\pi^0$
decays with additional two spurious clusters, we have performed a discriminant
analysis based on kinematical fit, testing of the signal and background
hypotheses and exploiting of the differences in kinematics of the $K_S$ decays
into $2\pi^0$ and $3\pi^0$. In a sample of about 1.7$\cdot 10^9$ $\phi \to K_S
K_L$ events we have found no candidates in data and simulated background
samples. Normalizing to the number of $K_S \to 2\pi^0$ events in the same
sample, we have set the upper limit on the $K_S \to 3\pi^0$ branching ratio
BR($K_S \to 3\pi^0) < 2.6 \cdot 10^{-8}$ at 90% C.L., five times lower than the
previous limit. This upper limit can be translated into a limit on the modulus
of the $\eta_{000}$ parameter amounting to $|\eta_{000}| < 0.0088$ at 90% C.L.,
improving by a factor two the latest direct measurement.
