  We have combined the perturbative unitarity and the renormalisation group
equations arguments in order to find a dynamical way to constrain the $g'_1$
coupling of the minimal $B-L$ extension of the Standard Model. We have analysed
the role of the $g'_1$ coupling evolution in the perturbative stability of the
two-to-two body scattering amplitudes of the vector boson and scalar sectors of
the model and we have shown that the perturbative unitarity imposes an upper
bound on the $B-L$ gauge coupling. We have made a comparison between this
criterion and the triviality arguments, showing that our procedure
substantially refines the triviality bounds.
