A machine has stations for continuous fish filleting. Decapitated gutted fish are placed with backs upwards and fronts foremost. A first station engages the fish and centers the fish relative to a vertical plane. Lower sides of the fish are arranged on opposite sides of the plane. A second station detects and registers vertical extents of lower edges and backs of the fish. A third station fixates backs of the fish and cuts slits in the backs. The slits extend at least along either side of protruding back fins. A fourth station has articulated cutters arranged on either side of the vertical plane for trimming parts of lowermost sides and edges of the fish. A fifth station has upper cutters positioned along the vertical plane for cutting meat free from vertebrae. A sixth station cuts vertically on either side of the vertebrae. A seventh station directs fillets outward.