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: The first pendent groups are typically according to the formula: —R1—SO3H, where R1 is a branched or unbranched perfluoroalkyl or perfluoroether group comprising 1-15 carbon atoms and 0-4 oxygen atoms, most typically —O—CF2—CF2—CF2—CF2—SO3H or —O—CF2—CF(CF3)—O—CF2—CF2—SO3H.