A method for transferring a continuously arriving web, specifically a paper or cardboard web, from a finished product roll to a new core rotating at the speed of web travel. The new core bears in the direction of web travel and before the finished product roll on a drum around which loops the web. The web is cut longitudinally, prior to running on the drum, for forming a transfer strip. Before reaching the new core, the transfer strip is severed from the advancing web and passed onto the new core. The web is subsequently cut across its entire width, wherein this cut originates from the longitudinal cut.A drum winder for accomplishing the method wherein the severing device for the transfer strip is arranged before the intake gap between the drum and the new core. A high-pressure water jet is used for severing the transfer strip from the web.