Background: Lorentz invariance is key in our understanding of nature, yet relatively few experiments have tested Lorentz invariance in weak interactions.Purpose: Obtaining limits on Lorentz-invariance violation in weak interactions, in particular rotational invariance in β-decay. Method:We search for a dependence of the lifetime of 20 Na nuclei on the nuclear spin direction.Such 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.Results: The experiment sets a limit of 2 × 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.Conclusions: No significant violation of Lorentz invariance is found. The result sets limits on parameters of theories describing Lorentz-invariance violation.