A sealing instrument (10) including two branches (15, 16) with sealing jaws (19, 20, 36, 37) acted on by a sealing voltage preferably between 80 and 120 volts. Tissue receptacles (53, 54) are separated from one another by a wall-like extension (24), which at its lower edge carries a cutting electrode (31), are defined between the branches (15, 16). A cutting voltage from 300 to 500 volts is applied between a branch (16) and the cutting electrode. When the branches are closed the grasped tissue is sealed simultaneously between the sealing jaws (19, 36 and 20, 37) and is severed by the cutting electrode (31). Even though the tissue is severed completely; for example after 0.3 to 0.5 seconds and the sealing requires more time, the rolls of tissue grasped in the tissue receptacles (53, 54) act as form-fitting protection of the vessel edges in the tool (12).