A new measurement of the rare, doubly radiative decay eta->pi^0 gamma gamma was conducted with the Crystal Ball and TAPS multiphoton spectrometers together with the photon tagging facility at the Mainz Microtron MAMI. New data on the dependence of the partial decay width, Gamma(eta->pi^0 gamma gamma), on the two-photon invariant mass squared, m^2(gamma gamma), as well as a new, more precise value for the decay width, Gamma(eta->pi^0 gamma gamma) = (0.33+/-0.03_tot) eV, are based on analysis of 1.2 x 10^3 eta->pi^0 gamma gamma decays from a total of 6 x 10^7 eta mesons produced in the gamma p -> eta p reaction. The present results for dGamma(eta->pi^0 gamma gamma)/dm^2(gamma gamma) are in good agreement with previous measurements and recent theoretical calculations for this dependence.
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