The invention discloses a method of continuous edge processing of plates and an edge processing device. According to the invention, plates (2;) are conveyed continuously in a conveying direction, whereby at least a first edge (15) of a plate Is provided with an edge profile by means of a rotating edge milling tool. A corner (16) connecting, the first edge and a second edge (17) of the plate is rounded at least partly by means of a rotating milling tool (12a, 12b) having a peripheral profile corresponding to a desired comer edge: profile of the plate. The rotating corner milling tool is controlled to be displaced along the continuously moving plate so if) at the rotating garner milling tool moves next to a corner to: he mimdeel1 and Is subsequently controlled to fee displaced simultaneouslyin the conveying direction (D) and m a transverse direction to Hie conveying, direction so that if follows a trajectory describing at least a part of: a desired rounding of the corner in a coordinatesystem fixed to the continuously moving plate.