In a method for mechanically removing intermuscular bones, so-called pin bones, from fillet parts of conveyed fish abdominal flaps for each fish are separated using a continuous, curved double separating cut. Each abdominal flap is simultaneously separated into two parallelly cut, completely free-moving parts having fish skin, which are conveyed away separate front one another. The first part is obtained as a narrow, curved pinbone strip, with a width corresponding to the row of pinbones and limited thereto. The second part is obtained as an abdominal flap meat body determined by the largest part of the separated abdominal flap, free of pin bones, with a cutting length having the curvature. An apparatus for performing the double separating cut of the abdominal flaps is formed by an abdominal flap cutting device which comprises two pairs of cutting tools which cut simultaneously for complete separation of the abdominal flaps, each said pair being designed to perform the double separating cut of the abdominal flaps. A guiding device has a guide which is height-adjustable in a height corresponding to the flank-side height of the fish. The guiding device holds the pairs of cutting tools, aligns them, and guides them to perform the curved double separating cut. The cutting tools of the pair of cutting tools are arranged with a distance which is adapted to the narrow width of the pinbone strip and corresponds to it.