A method for producing ultra-thin glass sheets is provided that results in glass sheets with high edge strength. The method includes: hot forming a continuous glass ribbon with a glass thickness from molten glass; annealing the glass ribbon with an annealing rate chosen based on the glass thickness; producing a laser beam focus area that is longer than the glass thickness; introducing filamentary defects into the glass ribbon using the laser beam so that the filamentary defects extend from one face to the opposite face and are spaced apart from one another along the breaking lines to produce transverse breaking lines and longitudinal breaking lines with margins each comprising a thickened bead; separating the beads along the longitudinal breaking lines and separating glass sheets by severing along the transverse breaking lines.