To provide an electrolyte polymer for polymer electrolyte fuel cells, made of a perfluorinated polymer having sulfonic groups, characterized in that in a test of immersing 0.1 g of the polymer in 50 g of a fenton reagent solution containing 3% of an aqueous hydrogen peroxide solution and 200 ppm of bivalent iron ions at 40.degree. C. for 16 hours, the amount of eluted fluorine ions detected in the solution is not more than 0.002% of the total amount of fluorine in the polymer immersed. The electrolyte polymer of the present invention has very few unstable terminal groups and has an excellent durability, and therefore, is suitable as a polymer constituting an electrolyte membrane for polymer electrolyte fuel cells and a polymer contained in a catalyst layer.