A hairdressing razor for cutting hair having an elongated handle and a cutting head joined to the handle, wherein at least one blade holder for at least one blade is provided in the cutting head. In order to achieve an improved cutting result and a longer blade service life, the invention provides for the longitudinal axis of the blade to be arranged at an angle to the longitudinal axis of the cutting head. A single recess is provided on at least one longitudinal side of the cutting head into which recess a free cutting region of projects without extending beyond the longitudinal edge of the longitudinal side when a blade is located in the blade holder, and wherein a length of the recess is smaller than half the length of the longitudinal side and wherein a length of the free cutting region in the recess is smaller than 15 mm.