A safety razor blade unit has an upper face, a bottom face, a front and a rear face. A plurality of cutting edges are positioned between a first guard surface and a first cap surface at the upper face. A frame element is formed separately from and connected to the rear face, the frame element has a second guard surface and a second cap surface. An auxiliary blade is supported by the frame element having an elongated cutting edge disposed between the second guard surface and the second cap surface. The elongated cutting edge of the auxiliary blade is directed generally away from the upper face of the blade unit. The second guard surface, the second cap surface, and the cutting edge of the auxiliary blade are at the rear face of the blade unit.