NOVELTY - A catalyst (C1) comprising an alloy supported on a chalgogen based carrier, is new. The chalcogen element is selected from sulfur, selenium and/or tellurium. The alloy (I) is made of component A (selected from palladium, iridium or rhodium) and component B (selected from molybdenum or tunsten).    USE - As a catalyst useful in a membrane-electrode assembly of a fuel cell.(claimed).    ADVANTAGE - By supporting the alloy on a carrier comprising sulfur, selenium, or tellurium improves the activity of a catalyst. The S, Se, or Te prevents oxygen in the air from being bound with the alloy, playing a role of promoting reduction of an oxidant. They also suppress fuel oxidation reaction, resulting in improvement of catalyst selectivity. Therefore, a cathode catalyst have high activity and selectivity for reduction reaction of an oxidant is obtained.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for following:    (1) a method of manufacturing the catalyst (C1) involving mixing a palladium/iridium/rhodium precursor, a molybdenum/tunsten precursor, and the carrier; filtering the mixture, drying the filtered mixture and heat-treating the dried mixture;    (2) a membrane-electrode assembly (E1) for a fuel cell, containing an anode, a cathode facing the anode and the catalyst (C1) and a polymer electrolyte membrane interposed between the anode and the cathode;    (3) a fuel cell system comprises electricity generating element; and separators disposed on each side of the membrane-electrode assembly; a fuel supplier supplying the electricity generating element with a fuel and an oxidant supplier supplying the electricity generating element with an oxidant. molybdenum/tunsten. The electricity generating element contains a membrane-electrode assembly, which contains an anode; a cathode facing the anode, where the cathode comprises a conductive electrode substrate and a catalyst layer (C1) on the conductive electrode substrate. The catalyst layer and a polymer electrolyte membrane are interposed between the anode and the cathode.