Improved upper limits are derived on the possible existence of the T-v
iolating (time-reversal) part of the tensor weak coupling constants, C
(T) and C(T)'. The previous measurements of the electron-neutrino dire
ctional correlation in the nuclear beta decay of He-6 are analyzed for
sensitivity to T-violating couplings. The results of the analysis are
presented in the context of previous beta decay limits on T-violating
tensor couplings and compared to somewhat similar limits from precisi
on electric dipole moment experiments.