The invention relates to an improved method and to an improved device (2) for producing a thin-glass strip (1) having a thickness of at most 300 micrometers, which provide for separating regions of increased thickness at the rims of the thin-glass strip (1), what are referred to as the borders (7, 8). In that context, high-mechanical quality edges (11, 12) are formed, and the formation of new secondary borders after separation from the strip-shaped glass melt (3) is prevented or at least the thickness of the secondary borders with respect to the original borders (7, 8) is reduced. In particular, after separation, permanent mechanical stresses in the glass are avoided as far as possible. To that end, the thin-glass strip (1) is drawn from a glass melt (3) or from a preform (18), the borders (7, 8) are separated from the thin-glass strip (1) by means of a separating device (9) and the resulting glass strip is cooled. In that context, the separation is carried out at a location along the direction of movement of the thin-glass strip (1) and at a point in time at which, during cooling of the thin-glass strip (1), the viscosity of the glass is in the range between 107 dPas and 1011 dPas, so as to round off the edges (11, 12), newly formed by the separation of the borders (7, 8), of the thin-glass strip (1).