To minimize the risk for injuries due to hooked hair catching teeth, but still have a reasonable hair-cutting efficiency, a cutting unit (107) for a hair-cutting device (100) having two blades (202, 206) moving relatively to each other with at least one of the blades (202, 206) being toothed is proposed, wherein at least some teeth (208) have a larger cross-sectional area (CA) at their free end (210) than at their end (212) making the junction with the blade (206), wherein the larger cross-sectional area (CA) is 0.32 mm2 or more and wherein the shape of the larger cross-sectional area (CA) is such that the tooth (208) surface oriented to face the surface (305) with hair (301) to be cut when cutting has a larger distance to the middle axis (M) than the equivalent surface of the blade-side-end (212).