First observation of η(1405) decays into f(0)(980)π0.

The decays J/psi -> gamma pi(+)pi(-)pi(0) and J/psi ->gamma pi(0)pi(0)pi(0) are analyzed using a sample of 225 X 10(6) J/psi events collected with the BESIII detector. The decay of eta(1405) -> f(0)(980)pi(0) with a large isospin violation is observed for the first time. The width of the f(0)(980) observed in the dipion mass spectra is anomalously narrower than the world average. Decay rates for three-pion decays of the eta' are also measured precisely.