We search for a dependence of the lifetime of $^{20}text{Na}$ nuclei on the nuclear spin direction. Such a directional dependence would be evidence for Lorentz-invariance violation in weak interactions. A difference in lifetime between nuclei that are polarized in the east and west direction is searched for. This difference is maximally sensitive to the rotation of the Earth, while the sidereal dependence is free from most systematic errors. The experiment sets a limit of $2times 10^{-4}$ at 90 % C.L. on the amplitude of the sidereal variation of the relative lifetime differences, an improvement by a factor 15 compared to an earlier result.
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