  The aim of this work was to determine the KS -> 3pi0 decay branching ratio
and a modulus of the eta000 parameter, defined as the ratio of amplitudes for
KS -> 3 pi0 to KL -> 3pi0 decays, which characterizes the CP symmetry violation
in this decay. The measurement has been carried out with the KLOE detector
operating at the phi-factory DAFNE in the Italian National Center for Nuclear
Physics in Frascati. The KS mesons were identified with high efficiency via
registration of these KL mesons which crossed the drift chamber without
decaying and then interacted with the KLOE electromagnetic calorimeter. The KS
four-momentum vector was then determined using the registered position of the
KL meson and the known momentum of the phi meson. Next, the search for the KS
-> 3pi0 -> 6gamma decay was carried out by the selection of events with six
gamma quanta which momenta were reconstructed using time and energy measured by
the electromagnetic calorimeter. To increase the signal over background ratio
after identification of the KS meson and requiring six reconstructed photons a
discriminant analysis is performed. It is based on kinematical fit, testing of
the signal and background hypotheses and exploiting of the differences in
kinematics of the KS decays into 2pi0 and 3pi0. Hence, we have obtained the
upper limit on the KS -> 3pi0 branching ratio at the 90% confidence level BR(KS
-> 3pi0)< 2.7 x 10^-8, which is almost five times lower than the latest
published result. The search for the KS -> 3pi0 decay presented in this work
failed to detect a signal of sufficient statistical significance. This upper
limit can be translated into a limit on the modulus of the eta000 parameter
amounting to: |eta000| < 0.009 at the 90% confidence level.
