A dental handpiece is disclosed including a turbine construction creating a radial in flow of air onto the impeller blades about the whole circumference of the turbine. This generates additional torque and avoids asymmetrical thrust on the impeller wheel. A pair of axially spaced air bearings support the turbine. Air supply to the bearings is controlled in such a way that the air bearings are floated before drive air is supplied to the turbine and after drive air to the turbine has been shut off. This ensures that the air bearings are always operational irrespective of the operational state of the turbine. The handpiece has an improved ergonomic shape, especially the shape and configuration of the front or drive head, which provides additional tooth clearance and a better field of view. An angled swivel connection to the umbilical cord is provided which reduces physical strain on the dentist's wrist. A self adjusting lock and key type torque connection between the dental burr and the chuck is provided which accommodates both conventional burrs and the burr of the lock and key arrangement. An auto stop arrangement for the turbine is disclosed which prevents a vacuum buildup during run-down of the turbine. The specific construction of the auto stop valve in accordance with the invention closes both the drive and exhaust air conduits.