  Data collected by the KLOE experiment in years 2001/2002 for a total
integrated luminosity of 410 pb$^{-1}$, corresponding to 17 million of produced
$\eta$'s from the $\Phi \to \eta\gamma$ radiative decay, have been analyzed to
look for the C-violating decay $\eta\to\gamma\gamma\gamma$. The signal is
searched in events with 4 photons in the final state by using the spectrum of
the most energetic photon. The background is evaluated from the data themself,
doing a fifth degree polynomial fit outside the signal region, and
extrapolating inside it. No signal has been observed and taking into account a
selection efficiency $\epsilon = 20.3 %$ we get from a likelihood fit
Br$(\eta\to\gamma\gamma\gamma) \le 1.6\times10^{-5}$ at 95% CL. The procedure
has a systematic ambiguity at the 35 % level.
