A method and a device for improving the outer surface quality by an in-line outer surface treatment of slabs, which are produced in a continuous process from strand casting to hot rolling, with a heating furnace arranged between a CSP-casting machine and a hot rolling train. A defined surface of the slab with a layer thickness per slab side of up to 4 mm is oxidized in a targeted manner by an oxidation device. An oxidation treatment of the slab surface is combined with the following processing in-line method steps: prior to the oxidation treatment the outer surface of the slab is freed of naturally occurring scale by a scale washer, after the oxidation treatment a created oxidation layer as well as the newly formed scale is cooled, mechanically broken up in a roll pair and removed from the surface of the slab by a scale washer.