A method for manufacturing a laminated glass panel, which includes at least two glass substrates and at least one intermediate layer made of a polymeric material arranged between the substrates, the method including in the following order: the bending of the substrates; the controlled cooling of the substrates; and the formation of a laminated assembly that includes the substrates and the intermediate layer; the cutting of the laminated assembly straight through the entire thickness thereof along a line on one of the main surfaces thereof, the controlled cooling including general controlled cooling and local controlled cooling of an area that includes the cutting line, the local controlled cooling being faster than the general controlled cooling.