Abstract The reaction π −p→ π 0 π 0n has been measured with a 648 channel hodoscope spectrometer for the detection of the four γ's from the π 0 decays. The π 0 π 0 D-wave is fully compatible with the f 0 contribution as it is determined in high-statistics π + π − experiments. The magnitude of the π 0 π 0 S-wave and the cosinus of its phase angle (relative to the known D-wave) are determined from fits to the π 0 π 0 angular distributions. Argand diagrams for the I = 0 amplitude S 0 are given for the range 1000 to 1500 MeV/ c 2. Two solutions exist. One exceeds the unitarity limit above 1200 MeV/ c 2. The other remains within the unitarity limit and is nearly elastic up to 1450 MeV/ c 2. It indicates an S 0 wave resonance around 1300 MeV/ c 2.