A hot-stamping device (1) is described, having a stamping device (2) for transferring a transfer layer (15u) disposed on a carrier layer (15t) of a hot-stamping foil (15) onto a substrate (14). The hot-stamping device comprises a heatable stamping roller (11) and a counter-pressure roller (12), between which a stamping gap (16) is realized, in which a stamped substrate (17) is realized, and comprising a separating device (3), disposed downstream, for separating the carrier layer (15t) from the stamped substrate (17). The separating device (3) has a separating element (20), which is realized as a bar-shaped hollow body, disposed on which there is a supply for a compressed gas (21). At least one longitudinal edge of the separating element (20) is realized as a perforated separating edge (20k) having outflow openings (20a) for the compressed gas (22), for the purpose of realizing a gas cushion between the carrier layer (15t) and the separating element (20). The separating edge (20k) is disposed transversely in relation to the running direction and parallelwise in relation to the top side of the coated substrate (17).