a method for machining a gas turbine rotor which is provided with a cooling air slot which concentrically extends around the axis of the gas turbine rotor and is supplied with compressed cooling air via axial cooling air holes which at the side lead into the slot base of the cooling air slot , and the opening of which is covered by bridges which are arranged in a distributed manner over the circumference and spaced apart from each other by gaps . a crack - resistant slot shape is achieved without intervention into the configuration of the bridges by a material - removing tool , particularly a milling tool , being lowered in the gaps between the bridges one after the other into the cooling air slot and in this way the slot base of the cooling air slot being machined and widened over the entire circumference .