A micrometer-sized oil droplet of 4-octylaniline containing 5 mol % of an amphiphilic catalyst exhibited a self-propelled motion, producing tiny oil droplets, in an aqueous dispersion of an amphiphilic precursor of 4-octylaniline. The tiny droplets on the surface of the self-propelled droplet were conveyed to the posterior surface and released to the aqueous solution. Thus the persistent movement becomes possible in this chemical system, because the processing of chemical energy to mechanical movement proceeds by consuming exogenous fuel, not consuming the oil droplet itself. The mechanism of the unidirectional motion is hypothesized in terms of an asymmetric interfacial tension around the surface of the oil droplet.