A method of fabricating a metal part by selectively melting a powder, the method including: building up layer by layer on a plate and simultaneously with the part, at least one holder and support element for the part, the element being spaced apart and distinct from the part and being separated therefrom by a gap filled with non-melted powder; after the part has been made completely, removing at least some of the powder remaining in the gap between the part and the element, for example by suction, blowing, or vibration; and separating the part from the plate.