It is an incongruous image, captured in a photograph on Ms Dayan's office wall: the chairman of the Palestine Liberation Organisation passing the time of day with the diminutive daughter of one of Israel's most revered warriors, Moshe Dayan.
Yael Dayan, 54, is the only Israeli member of parliament to have taken advantage of new laws liberalising unofficial contacts with the PLO by going to Tunis last January to meet the Chairman himself. Now more and more Labour ministers are following her lead, saying that direct talks are the only possible solution to the Palestinian question.
What would General Dayan have thought? 'He asked many times to talk to Arafat, in the days when they were still terrorists. Arafat refused. In his later years my father realised we had to get the hell out of there - let them run their own lives.'
But what would the general have thought about his daughter's present to Mr Arafat? The photograph on her wall shows the PLO chairman happily accepting a copy of Ms Dayan's own book, My Father, His Daughter, in which she catalogues her father's adulterous relationships - with, among others, a schoolfriend of hers - and his notorious greed.
Ms Dayan shows rare signs of discomfiture. 'A book is a book. I am not a censor. I do not choose my readers. Anyway, there is no criticism of my father in the book . . . not in the total sense - not of his political life; and not, really, in his personal life either. There is nothing in it that was not in the newspapers, after all.'
Yael Dayan is certain always to be known as 'Dayan's daughter'. Her profile evokes his sharp features with uncanny accuracy - only the black eye- patch is missing. Her ambiguous reaction to her father's family betrayals has failed to shake her deep-down adoration and respect for the man who used to take her as a child to the top of a building in Jerusalem to peer through his binoculars at Jordanian soldiers on the other side.
His influence is clearly present in her readiness to embrace controversy. Beside the photograph of her with Mr Arafat is another of her, topless, sunbathing on a Tel Aviv beach on Yom Kippur. Male sexism is very much behind the many vicious attacks on her since she became an MP, she says.
But 'the religious' are her biggest problem. Ms Dayan says her greatest joy of the year was watching 'the religious' splutter into their beards when she brought gays and lesbians to the Knesset to promote homosexual rights. (She told them King David was gay, too, which did not help.) 'The religious feel very deeply that for a man to sleep with another man is as bad as sleeping with an animal. They say it deserves the death penalty.'
Again, what would her father have thought of her stands on these matters? 'He couldn't have cared less. His problem was that he probably didn't know that there were laws discriminating against them. He took it for granted that equal rights existed.'
Ms Dayan says that it is because Israel continues to 'take for granted' the predominance of security concerns that most Israelis today fail to see the need for civil rights for Palestinians. 'It is inconceivable that we should still have to discuss the Palestinian right to self-determination. We are still doubting that they are people. This is so stupid it is like an ostrich burying its head.'
For many Israelis, Moshe Dayan epitomised the proud image of the Zionist nation-builder. The Prime Minister, Yitzhak Rabin, of the same generation, has tried of late to evoke the pride of nation-building as a palliative for the country's current problems. But Yael Dayan speaks for a different generation. 'We are 45 years old. We are a nation - it is not a question of nation-building any more. It is a demagogic thing - mythical. The feeling that the whole world is against us - it is nonsense.'