An outer sleeve for a double-walled cup and a process for manufacturing the outer sleeve are described, in which a flat-lying blank made from a paper material is joined in a tube shape by means of the overlapping of two longitudinal edges of the blank, and in which the outer sleeve in this form is provided with an inwardly rolled curled part. The curled-in part is glued or sealed onto the inside of outer sleeve in the area of the overlap.