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This invention, which reduces elution of cobalt from a positive-electrode active material, provides a positive-electrode active material that is used in a nonaqueous-electrolyte secondary battery and contains a lithium-containing transition-metal oxide. Fluorine and at least one element selected from among zirconium, titanium, aluminum, magnesium, and the rare-earth elements are bound to the surface of said lithium-containing transition-metal oxide, which contains cobalt and has an average particle size of 10 µm or less.