NOVELTY - A dispersion liquid (A) of reversed micelle (100a-100d) containing microparticles containing primary metal oxide (5) which does not have oxygen defect is prepared. A dispersion liquid (B) of the reversed micelle containing platinum ion (6) is prepared. The obtained dispersion liquid (A), dispersion liquid (B) and sacrificial agent are mixed, and irradiated microwave, such that at least one surface of microparticles containing primary metal oxide is reduced to secondary metal oxide having oxygen defect, and outermost layer containing platinum is formed, to obtain catalyst fine particles.    USE - Manufacture of catalyst fine particles used for manufacturing carbon-supported catalyst microparticles (claimed) for gas-diffusion electrode for fuel cell.    ADVANTAGE - The method efficiently provides catalyst fine particles having excellent catalyst activity within short period of time.    DETAILED DESCRIPTION - A dispersion liquid (A) of reversed micelle containing microparticles containing primary metal oxide which does not have oxygen defect is prepared. A dispersion liquid (B) of the reversed micelle containing platinum ion is prepared. The obtained dispersion liquid (A), dispersion liquid (B) and sacrificial agent are mixed, and irradiated microwave, such that at least one surface of microparticles containing primary metal oxide is reduced to secondary metal oxide having oxygen defect, and outermost layer containing platinum is formed by reducing platinum ion on the secondary metal oxide, to obtain catalyst fine particles. An INDEPENDENT CLAIM is included for manufacture of carbon-supported catalyst microparticles, which involves mixing dispersion liquid (A), dispersion liquid (B), sacrificial agent, carbon support, and irradiating microwave.    DESCRIPTION OF DRAWING(S) - The drawing shows the structure of cross-section of reversed micelle for preparing dispersion liquid containing microparticles with primary metal oxide.    Hydrophilic group (1)    Lipophilic group (2)    Surfactant (3)    Microparticles containing primary metal oxide (5)    Platinum ion (6)    Reversed micelle (100a-100d)