Abstract: A cutter for removing a tough surface layer from pieces of material, more specifically for skinning fish, particularly fillets of fish. By means of a roller, the pieces of material are conveyed past a stationary cutter which removes the surface layer by cutting in between the latter and the piece of material, the surface layer passing between cutter and roller while the piece of material passes above the cutter. The cutter has adjacent its edge a projecting wall portion extending transversely of the travelling direction of the pieces of material and away from the cutter side opposite the roller.