1. First remove the skin from the monkfish tail. Put the tail belly-side down on a board. Release and pull back some of the skin at the wider end of the tail so that you can get a sharp, flexible-bladed knife underneath to cut through the fine dorsal spines.
2. Grab hold of the wider end of the tail in one hand and the skin in the other and briskly pull it away, down over the tail.
3. Remove the two fillets by cutting along either side of the thick backbone with a sharp, thin-bladed, flexible knife, keeping the blade as close to the bone as you can.
4. Pull off the thin membrane that encases the fillets, releasing it with the knife where necessary.
5. Cut the fillets across into thin slices for ceviche or use according to your recipe.