TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The catalyst comprises (wt.%) metal (M) (15-40), cobalt (Co) (20-50), and element (Ch) (10-65). The chalconide (Ch) has a nanowire shape. Preferred Components: The metal is metal chloride, metal acetyl acetonate, and metal nitrosylnitrate. The source of the cobalt is selected from cobalt acetate, cobalt nitrate, cobalt chloride, cobalt acetyl acetonate, and cobalt carbonyl. The chalconide supplying material is selected from sulfur powder, selenium powder, tellurium powder, sulfurous acid, selenic acid or telluric acid. Preferred Method: The drying is performed at 200- 300degreesC. The heat-treating is performed at 300-400degreesC. In the mixing, a carbon-based material is further added to form the catalyst supported on the carbon- based material. The mixing comprises: anodizing an aluminum thin membrane to form an aluminum oxide thin membrane having pores; mixing the source of the metal, the source of the cobalt and H3BO4; forming an alloy comprised of the metal and the cobalt around the pores of the aluminum oxide thin membrane by electrodeposition; removing the aluminum oxide to form a nanowire shape of the alloy; and mixing the nanowire-shape of the alloy with the chalconide-supplying material. Preferred Definitions:    M=Ru;    Ch=Te.    EXAMPLE - An aluminum oxide thin membrane with micropores was prepared by anodizing an aluminum thin membrane with purity degree of 99.999% in two steps. The first anodizing treatment was performed by applying a stable voltage of 40V into an oxalic acid aqueous solution (0.3M) at 10-15degreesC for 3 hours. The first anodized aluminum thin membrane was mixed with H3PO4 (0.4 M) and H2Cr2O4 (0.2 M) at 50-80degreesC to prepare a solution. The mixed solution was secondly anodized. The second anodizing treatment was the same as the first one except that it was performed for 10 hours. The prepared aluminum oxide thin membrane was dipped in a 5% phosphoric acid solution at 50-80degreesC for 20 minutes to remove unnecessary materials, forming micropores in the aluminum oxide thin membrane. The aluminum oxide thin membrane with micropores was mixed with CoSO4 (1.2 mol/l), K2RuCl (0.012 mol/l), and H3BO4 (30-40 g/l), preparing a mixture solution with pH of 2.0. The mixture solution was electrodeposited at 8 V. The electrodeposition was performed at room temperature. It also was performed by using three-electrodes, potentiostatic control, and direct current (DC). A saturated calomel electrode (SCE) was used as a reference electrode. A platinum plate was used as a counter electrode, and an aluminum oxide thin membrane coated with Ag was used as a working electrode. When the aluminum oxide thin membrane with micropores was electrodeposited, a ruthenium-cobalt (Ru-Co) nanowire was formed on it. The aluminum oxide thin membrane with the Ru-Co nanowire was annealed at 700degreesC under an Ar atmosphere for 20 minutes. The thin membrane having the ruthenium-cobalt alloy was put in a KOH aqueous solution to remove an aluminum oxide. The nanowire-shaped ruthenium-cobalt alloy and telluric acid were added to ethanol, and then mixed together. The resulting mixture was dried at 250degreesC and heat-treated at 350degreesC to give the cathode catalyst (test). The catalyst had high activity and excellent selectivity for reduction of an oxidant, and was capable of improving performance of a membrane-electrode assembly for a fuel cell, and a fuel cell system and a membrane-electrode assembly including the same.