For the finish machining of turbine blades cast in titanium aluminide, the feeders (3) and runner portions (6) yielded by the casting process remain on the blade and serve as auxiliary clamping structure for clamping the blade to the workpiece carrier (15). In a position corresponding to the reference points for machining, clamping surfaces (12) with conical recesses (13), followed by threaded holes (14) are produced on the runners. For clamping the workpiece to a workpiece carrier (15), spring-loaded taper centering sleeves (18) arranged in the workpiece carrier or clamping bolts (21), respectively, engage the conical recesses and threaded holes, to enable the blade to be clamped and machined by way of the auxiliary clamping structure in the position corresponding to the reference points.