Some of the Middle East clichés are back in vogue, among them the notion that an Arab-Israeli “peace process” will spark a regional domino effect and return a Garden of Eden to Mesopotamia.

Nowhere is this trend welcomed more than at Turtle Bay, where process — any process — is almost as loved as peace itself, and where doing something about the Israelis and the Palestinian Arabs is an obsession.

In 2002, as suicide bombers were detonating themselves daily in Israeli cities, clueless television reporters signed off broadcasts filled with bloody images by saying, “Only time will tell how this will affect the peace process.”

On March 22 of that year, the Arab League met in Beirut to adopt as its own a heretofore-sketchy “Saudi initiative.” With the renamed “Arab plan” — voilà — a peace process was reborn.

It essentially died the next day, when suicide bombers killed 29 Israelis celebrating the Seder at Netanya’s Park Hotel. Israel’s prime minister at the time, Ariel Sharon, launched a military operation that essentially ended the murderous campaign, and proved wrong the cliché that there are no military solutions to terrorism.

The Saudi initiative remained, and is now the centerpiece of a renewed effort among peace-processors. Yesterday, no less than Prime Minister Olmert said the plan includes positive “elements” that may become a basis for regional talks. As in 2002, the Saudis are filling a vacuum by being the only game in town for those, including the unpopular Mr. Olmert, seeking a process in lieu of solutions.

Western diplomats, who are banned from Mecca unless they convert to Islam, make pilgrimages to Riyadh. The Arab League will meet there next week, hosting among others Secretary General Ban. Mr. Ban’s trip will also include stops in Jerusalem and Ramallah. In preparation, Mr. Ban will meet Wednesday in New York with Israel’s foreign minister, Tzipi Livni, and defense minister, Amir Perez.

Coming into office, Mr. Ban talked about the centrality of the Arab-Israeli dispute. He modified that statement somewhat since then, saying Friday that resolving it would create a “conducive political atmosphere for the resolution of other issues in the Middle East.”

Over the weekend, Mr. Ban’s entire top team of undersecretaries-general met at the Greentree Estate in Long Island to assess internal Turtle Bay changes and “reaffirm the need to speak with one voice and act with common purpose,” as one participant, who did not want to be identified, explained to me.

But common purpose is hard to achieve at the United Nations. The new undersecretary general for political affairs, Lynn Pascoe, is a former State Department East Asia specialist who speaks Mandarin perfectly, but has yet to study Arab nuances.

Meanwhile, Norwegian diplomat Terje Roed-Larsen, a veteran Middle East hand, is expected to report to Mr. Ban this week on his weekend trip to Saudi Arabia. Unlike some enthusiastic U.N. predecessors, Messrs. Pascoe and Roed-Larsen are undoubtedly aware of the limitations the Saudi plan represents to Israelis.

Mostly, Israelis are concerned that the Jewish nature of their state would be ended by a provision calling upon all descendants of Arabs who fled Palestine in 1948 to return, if they wish. Under Syrian pressure, the plan also dictates a strict adherence to pre-1967 ceasefire borderlines, excluding any creativity involving land exchanges.

Mostly, however, the plan aims at solving a problem that already was only marginal to the region’s ills when it was launched in 2002, and is even less important now.

Reasonable Americans who watch the bloodshed in Iraq see a war that has little, if anything, to do with the Arab-Israeli dispute. Although the Baker-Hamilton plan stressed it, King Abdullah of Jordan’s message last week about the centrality of the Palestinian Arab cause was received coolly by Congress.

In Iraq, as elsewhere in the region, there is a schism that stems from Iran’s drive to become a top regional power, and the Arab forces that fear and fight it. That schism is “very deep, and is only in its early stages,” Israel’s deputy defense minister, Ephraim Sneh, told me last week.

It is a schism that does not arise out of the Israeli-Arab dispute, but instead drives the dispute into the hands of the extremists, making any diplomatic solution almost impossible. A new Arab-Israeli process based on old ideas will therefore be very appealing to regional leaders, some State Department types, and for the United Nations. It will do little, however, to solve the region’s problems.