The present invention relates to a polyaromatic polymer that comprises multifunctional aromatic moieties MA, cationic groups CG and bifunctional aromatic moieties BA, wherein one or more CG and one or more BA form a linear unit L, and MA is connected to 3 to 6 linear units L. MA, CG and BA are defined as described in the specification. Furthermore, the present invention relates to a neutral precursor of the polyaromatic polymer and to an anion exchange membrane that comprises a polyaromatic polymer according to the invention.