A mass-independent partial-wave analysis of the reaction pi(-)p -->eta
pi(0)n is performed in the eta pi(0) mass range above 1.6 GeV. The an
alysis employs the S, P, D, F, and G waves and is based on experimenta
l data collected with the GAMS-2000 multiphoton spectrometer in a 38-G
eV/c pion beam extracted from the 70-GeV accelerator of IHEP. A resona
nce with quantum numbers J(PC)=4(++) and I-G=1(-) is observed in the G
wave. Its mass and width are measured to be M=2010+/-20 MeV and Gamma
=370+/-80 MeV. The mechanism of the observed a(4)(0)-meson production
is dominated by natural-spin-parity exchange in the t channel. The mea
sured unnatural-to-natural cross-section ratio is 0.60+/-0.16.