Heat the oil in a large pan and fry the onion.
Add the tomato purée and the vinegar; cook over a low heat for 5 minutes.
Salt and pepper the turbot fillets, put them in the pan on the bed of tomato and vinegar and sprinkle on the chopped olives.
Cook covered over a low heat for 8 minutes.
At the end of the cooking, powder with the herbs and serve.