The present invention relates to a mesh or membrane covering (2) based on biological material, for example collagen, or biosynthetic material for prostheses (1), in particular for a breast prosthesis (1), said prosthesis (1) having a rear surface that, when applied, is faced towards the person on whom (1) is applied, said covering (2) being characterized in that it provides a fixing system (4; 3) for fixing to said prosthesis (1), said fixing system providing a plurality of teeth or petals (4) or outer perimeter edge foldable on said rear surface of the prosthesis (1) by means (5). The invention further relates to a method for fixing said covering to a prosthesis, a prosthesis comprising said covering and a process for making said covering.