  A precise measurement of the Dalitz plot parameter, alpha, for the eta->3pi^0
decay is presented. The experiment was performed with the Crystal Ball and TAPS
large acceptance photon detectors at the tagged photon beam facility of the
MAMI-B electron accelerator in Mainz. High statistics of 1.8*10^6 eta->3pi^0
events were obtained, giving the result alpha = -0.032 +/- 0.002(stat) +/-
0.002(syst).
