The invention relates to a cutting member (7) for use in a device for shaving hair. The cutting member comprises a metal substrate (15) which is provided with a cutting edge (9). At least a portion of the substrate including the cutting edge is provided with a protective coating (19). According to the invention the coating (19) comprises a plurality of stacked pairs (21) of layers, wherein each pair of layers comprises a first layer (23) mainly comprising carbon (C) and a second layer (25) mainly comprising a metal, and wherein each pair of layers has a thickness (TP) between 1 and 10 nm. The second layer preferably comprises Cr, Nb, Mo, Ti, V, or W. As a result, the coating has a superlattice structure which provides the coating with physical properties which are superior to the properties of the individual materials of the layers. In an embodiment wherein the second layer comprises Cr and each pair (21) of layers has a thickness of 1.8 nm, the coating (19) has a hardness that is approximately four times the hardness of Cr and provides a coefficient of friction between the cutting member (7) and the hair to be shaved which is considerably lower than the coefficient of friction which would be obtained without the coating.