  Polarization of societies is getting more and more attention from researchers
working at the intersection of many fields, because it seems to be a defining
feature of many public domains. In this paper, we are going to investigate how
the unwillingness to yield to the group pressure, also known as independence,
influences this phenomenon. In particular, we would like to answer the question
whether independent choices of people could alter the dynamics of a system that
otherwise would become polarized. A modified version of the $q$-voter model
will be used for that purpose. From our findings it follows that the impact of
independence is at least two-fold. At low independence levels the
consensus-polarization transition between two antagonistic groups sets in
quicker than in the absence of independence. Higher levels induce additional
transition in the system, from a polarized state to a disordered one.
