It was a highly polished act which played all the big capitals for 29 years - the Egyptian-Israeli diplomatic tango.

One ambassador comes in this door, the other enters in that door. Noses in the air, they glide smoothly through the crowd. No flicker of recognition passes between them. Perfectly, they execute their social duties without acknowledges each other.

But now that their bosses, the president of Egypt and the prime minister of Israel, was waltzing so happily, the ambassadors of Israel and Egypt must warm up their act. And so ABC news person Barbara Walters, one of the impresarios of the main event, is staging the Washington company.

On Sunday, she and ABC News and Sports president Roone Arledge are giving "a small, informal dinner" at the Madison Hotel, to which they are inviting Israel's Ambassador Simcha Dinitz Egypt's Ambassador Ashraf Ghorbal.

This used to be a social no-no. Sallie Vance, wife of the Secretary of State, once even altered world geography to avoid this. Inviting wives of chiefs of diplomatic missions to tea in small groups, she declared that Israel was in Europe, and Mrs. Dinitz ought to attend tea with the European group, not the Middle Eastern, where the Arab wives would be.

Chief of Protocal Evan Dobelle said that the best you could do at gatherings to which the entire diplomatic corps would be invited would be to scat them far apart.

Barbara Walters plans to seat them cozily close, probably one on either side of her, so they can chat.

This is absolutely the first time they will talk," said Walters, who sees the event not as an opportunity to glean more news - "there will be no cameras, not even ours" - but "to bring two friends together."

She gave the history of the event:

"What happened was that when we were in Egypt, we asked President Sadat, would his ambassador be able to meet the Israeli ambassador and talk, and he said, 'Why not?' We asked them to be on 'Issues and Answers' together, but they said they wouldn't want the first meeting between them to be on television, but that is I were to give a private party, for instance they would both come."

According to the embassies, nobody had instructions not to speak previously, but, on the other hand, there was nothing personal in the fact that they never did.

"We didn't have a policy not to talk," said an Israeli embassy spokesperson. "But we didn't, because we knew they wouldn't talk to us."

"We had no specific guidelines, but everyone understood how it was to be," said an Egyptian embassy spokesperson, leaving one wondering if the whole act had been a terrible misunderstanding.

But, no. The Egyptian spokesperson said that last week, Egyptian diplomats were instructed by Cairo that "socially it is approved" now to stop cutting Israelis.

Walters said she had witnessed the cutting act some years ago in a television studio, where both ambassadors had come to pay tribute to President Nixon's "Ambassador of Love," Pearl Bailey. "It made me very uncomfortable," Walters recalled.

At her party, there still be no protocol at all, she said. She hasn't even decided definitely exactly where the two will sit for their chat. "I wonder how Elsa Maxwell did it?" She asked yesterday, "I suppose she had 32 assistants."