We propose a new method to control the familywise error rate (FWER) in linear Gaussian models. Our method relies on a lasso-type estimator and can be used for all n x p full-rank design matrices. We provide an explicit and non-asymptotic choice for the lasso tuning parameter that controls the FWER. Numerical experiments highlight the performances of our approach compared to the state-of-the-art procedures. An application to the detection of metabolites in metabolomics is provided..