A method for fabricating a metal member having a plurality or multitude of fine holes comprises forming a repeatedly usable master which includes a conductive substrate and non-conductive portions used to form the fine holes and fixedly deposited on the conductive substrate, subjecting the master to electrodeposition to form an electrodeposition film which has non-electrodeposited fine holes in position corresponding to the non-conductive portions, and separating the electrodeposition film from the master. In the master formation step, the non-conductive portions are so formed to have projections from the surface of the conductive substrate. The electrodeposition is effected so that the electrodeposition film is deposited about the side surfaces of each projection as exposing at least a top of the projection. The fine holes of the separated electrodeposition film have invariably a constant dimensional accuracy without suffering any influence of the electrodeposition conditions. The formation density of the fine holes is free of any limitation as will be caused by the thickness of the electrodeposition film.