A method is provided for making a crosslinked polymer electrolyte, typically in the form of a membrane for use as a polymer electrolyte membrane in an electrolytic cell such as a fuel cell, by trimerization of nitrile groups contained on groups pendant from the polymer. The resulting polymer electrolyte membrane comprises a highly fluorinated polymer comprising: a perfluorinated backbone, first pendent groups which comprise sulfonic acid groups, and crosslinks comprising trivalent groups according to the formula: ##STR00001## The first pendent groups are typically according to the formula: --R.sup.1--SO.sub.3H, where R.sup.1 is a branched or unbranched perfluoroalkyl or perfluoroether group comprising 1 15 carbon atoms and 0 4 oxygen atoms, most typically --O--CF.sub.2--CF.sub.2--CF.sub.2--CF.sub.2--SO.sub.3H or --O--CF.sub.2--CF(CF.sub.3)--O--CF.sub.2--CF.sub.2--SO.sub.3H.