A razor blade unit including a blade housing to hold at least one blade with a cutting edge, and a cover connected to the blade housing. The cover faces the back edges of the blades, i.e., the edges opposite from the cutting edges. The blade housing has positioning notches to support the cutting edges. In addition, the cover can have recesses to support the back edges of the blades and an elastic component, which exerts a pressing force on the back edges of the blades.