A gas bag module comprises a gas bag with a gas bag wall having a front wall serving as an impact surface for an occupant, where, in an inflated state of said gas bag, the front wall has a centric orifice as a transition to an indentation. The indentation is formed by restraining a center section of the gas bag wall during inflation and preventing the center section from moving freely. The orifice is surrounded by a stabilizer defined by a closed ring in a region of the orifice and the stabilizer is a part separate from the gas bag wall.