A new measurement of the ratio of the CP-violating amplitudes for K(L)
--> 2pi0 and K(L) --> pi+pi- is reported. The measured value for R =
\eta00/eta+-\2 is 0.9878 +/- 0.0026 +/- 0.0030, where the first error
is the statistical uncertainty and the second is the estimate of the s
ystematic uncertainty. This gives a value for the parameter describing
direct CP violation: Re epsilon'/epsilon = (2.0 +/- 0.7) X 10(-3).