In two directed forgetting experiments subjects were required to forget some false memories. In experiment 1 the 13 words from list 1 were related to a non presented critical word whereas the 13 words from list 2 were unrelated. In experiment 2 both list 1 and 2 had 18 words: 6 words related to a first critical word. 6 related to a second critical word, and the last 6 words to a third critical word. None of both experiments found inhibition of such false memories suggesting that is not possible to forget a false memory. Even in experiment 2 there was a trend to the appearance of a postsuppression rebound that would indicate that the attempt of forgetting a false memory could be even counterproductive.