Place the fish on a large cutting board so the head is facing your non-dominant hand.
Hold down the fish's head. Position a flexible fillet or boning knife behind the head of the fish. Position the knife on the side that does not contain the guts.
Cut straight down. Without removing the knife, turn it at an angle toward the tail, and finish the cut over the backbone from the head to the tail.
Using the tip of the knife, cut the arc on the back of the fish's paunch to remove its guts. Dispose of the guts. Remove the egg sacs carefully, and save them for additional dishes.
Position the cleaver where you made the first downward cut. Make a swift and firm cut to remove the head.
If you plan to cook the head, use the knife to cut the thin membrane that holds in the gills, and then remove the gills. Otherwise, dispose of the head.
Hold the fillet at the tail, and slip the knife along the tail to the head to skin the fillet.
Neatly trim the edges of the fillet.