In a fileting process for fish of the Siluridae species, for instance, catfish (Ictalurus punctatus), the bone plate present in the area of the dorsal fin of these species for supporting the dorsal spike is first undercut from the dorsal area without cutting through its connection to the bone structure, in order to obtain largely trim-free filets. This takes place by means of a cutting tool that makes incisions under the bone plate up to the ventral bones, so that, in the subsequent cutting free of the filet meat from the ventral bones, the outer parts of the bone plate accumulate separately from the filet meat.