Newsnight has obtained the first pictures of Kurdish soldiers being trained by Israelis in Northern Iraq, as well as an interview with one of the former commandos who carried out the work.
When the former Israeli special forces soldiers were sent to Iraq in 2004 they were told they would be disowned if they were discovered.
Their role there was to train two groups of Kurdish troops.
One would act as a security force for the new Hawler International Airport (near Erbil) and the other, of more than 100 peshmerga or Kurdish fighters, would be trained for "special assignments", according to one of Newsnight's interviewees.
An Israeli security consulting form called Interop acted as the main contractor for the Hawler airport project and set up two subsidiaries (Kudo and Colosium) to carry out work in Iraq.
Kudo and Colosium described themseleves as Swiss-registered companies.
In addition to the training, Kudo provided quad bikes, communications equipment and security fencing.
One of the founders of Interop, and its Chairman until 2003, was Danny Yatom, a former Head of Mossad - the Israeli foreign intelligence service and now an MP.
He told Newsnight today: "I was not aware of what was done in 2004 and 2005 because I cut all contacts with the company when I entered the Israeli parliament in 2003."
During 2004-5, Interop and Kudo were run by Shlomi Michaels, a former head of Israel's counter-terrorist unit. Contacted by Newsnight, Mr Michaels declined to comment.
Newsnight was told by the Israeli interviewee involved in the training that senior Kurdish officials were aware of their nationality, but not the troops being trained.
The sensitivities for the Kurdish authorities are serious, since their political enemies have long accused them of being in cahoots with Israel.
Iran and Turkey are concerned about a Kurdish state emerging in Northern Iraq
The Kurdish authorities have previously denied allowing any Israelis into northern Iraq.
The Israeli trainer says: "You know, day by day it's a bit tense because you know where you are and you know who you are. And there's always a chance that you'll get revealed.
"My part of the contract was to train the Kurdish security people for a big airport project and for training, as well as the Peshmerga, and the actual soldiers, the army.
"We were training them in all kinds of anti-terror lessons, anti-terror, security airport, training them with long rifles, pistols; telling them, teaching them tactics like shooting behind doors, behind barricades, shooting from the left, shooting from the right, shooting from windows, how to shoot first, how to identify a terrorist in a crowd.
"That's clearly special assignments. That's only training that special units get for special assignments.
"We crossed the border from Turkey and one of the intelligence officers passed us by, through the border, without stamping our passports.
"So you reckon that if two guys from the intelligence service knew we were Israelis and they saw our passports as well, the leadership knew as well - I mean their bosses, that's natural."
"The second Israel"
Khaled Salih, a spokesman for the Kurdistan Regional Government, says: "These are not new allegations for us. Back in the sixties and seventies we were called 'the second Israel' in the region and we were supposed to be eliminated by Islamist nationalist and now Islamist groups.
"They look for internal enemies and we are the easiest to target. These kind of speculations have been around in the region for more than 30 years."
The Kurdish authorities have long been accused of being in cahoots with Israel
The Kurdistan region sits at a strategic crossroads. To the east is Iran, to the north-west Turkey. Both countries have significant Kurd minorities and are worried about a Kurdish state emerging in northern Iraq.
The authorities there have accepted that for now and that they must remain part of a federal Iraq.
As they develop their region, the Kurds have opened an international airport at Irbil (Hawler in Kurdish).
It now boasts dozens of international flights each week and it is at Hawler International that the Israelis began their work.
With Iran becoming Israel's principal enemy, there have been reports of Israelis using Kurdish areas of Iraq to increase its strategic options.
One constraint facing the Israelis, should they ever want to hit Iran, is distance. Most Israeli jets are short range and they have few in-flight tankers. Some studies have suggested that Israel could make refuelling stops at a modern airfield in Kurdistan.
If the Israelis ever planned to use Hawler airport as an emergency refuelling stop, it has now been compromised by Israeli press reports.
After finishing their training, Kurds sang their national anthem while marching behind one of the Israelis.
Israeli Government spokesman, Mark Regev, told Newsnight that the Investigations Division of the Israeli Ministry of Defence had passed the details of this case to the Israeli police to see if there had been any violation of export laws.
He added: "We have not authorised anyone to do any defence work in Iraq... If information is brought and there's clear evidence that people broke our law, of course I expect them to be prosecuted."
MARK URBAN'S REPORT WAS SHOWN ON NEWSNIGHT ON TUESDAY, 19 SEPTEMBER, 2006