The invention relates to a medical turbine handpiece, in particular a dental turbine handpiece, having a drive shaft rotatably mounted in the front end region of the handpiece and to which a tool can be connected, as well as a turbine wheel arranged so as to be non-rotatable on the drive shaft and is arranged in a turbine chamber realized in the end region, into which turbine chamber a supply line for a flowing pressure medium for driving the turbine wheel opens out at an inlet opening and from which turbine chamber a removal line extends at an outlet opening, wherein at least one cross connecting channel for the pressure medium is realized in the wall of the turbine chamber, the cross connecting channel connecting the axially remote edge region of the turbine chamber to a region of the turbine chamber that is axially close to the drive shaft.