Fillet a very fresh mackerel but leave the skin intact. Place the two fillets flesh-side down on a thick bed of salt in a large, flat dish and cover them completely with more salt. Leave for at least 30 minutes, ideally for 3-4 hours.
Wash the fillets and pat dry with kitchen paper, then remove all the bones, with tweezers, if you wish.
Put about 120ml/4 fl oz/½ cup rice vinegar or white wine vinegar in a flat serving dish. Lay the fillets flesh-side down in the dish and sprinkle more vinegar over them. Leave the fillets to marinate for 10 minutes, then drain.
Pat dry with kitchen paper and carefully remove the transparent skin with your fingers, working from head to tail, leaving the silver pattern on the flesh intact. For sashimi, cut the fillets crossways into 1-2cm/½-¾ in thick slices.