A dental milling machine has idle receptacles arranged in a storage chamber for storing a plurality of blanks. The blanks each are placed without frame as a frameless blank in the idle receptacles. A transfer device with a transport arm is arranged in the storage chamber. A work chamber adjoins the storage chamber. A transfer opening is arranged between work chamber and storage chamber. The transport arm grips a frameless blank stored in the storage chamber and moves it through the transfer opening into the work chamber. A workpiece holder arranged in the work chamber receives the frameless blank from the transport arm. The workpiece holder grips the frameless blank by a receiving rim of the frameless blank. The workpiece holder, for milling the frameless blank in the work chamber by a milling tool, holds by a clamping action the frameless blank at the receiving rim.
