Members of the unit were celebrating their last day in Hebron
An Israeli court has convicted two border guards over the unlawful killing of a Palestinian teenager in the West Bank town of Hebron in 2002.
Imran Abu Hamdieh died after the two men, Shahar Botbeka and Denis Alhazov, pushed him from the back of a military vehicle travelling at 50mph (80km/h).
Earlier this year, another member of their unit was jailed for six and a half years, but he fled the country.
A fourth officer was jailed for four and a half years in a plea bargain.
Mr Abu Hamdieh was seized from outside his home in Hebron on 30 December 2002.
He suffered serious head injuries when members of the border police unit - celebrating the end of their posting in Hebron - made him jump from their jeep as it sped through the streets.
In Israeli law, the offence the policeman was convicted of, which translates from Hebrew as "killing", is usually used to denote cases where the death was not premeditated, in contrast to murder.
Botbek and Alhazov are due to be sentenced in December.
Court documents described their actions as a rampage of cruel abuse.
They grabbed several Palestinians off the street and drove them to remote locations to beat them.
Imran Abu Hamdieh was picked up late in the evening. The border policemen beat him inside the vehicle and then opened the back door and ordered him to jump out, but he refused.
As the jeep reached 70-80km an hour, the policemen managed to prise his grip loose, and pushed him out of the vehicle and it sped off.
The BBC's Tim Franks in Jerusalem says Hebron is a tense place even in normal times; it is the only city in the West Bank which also has an enclave of Jewish settlers living there, guarded by a large Israeli military presence.
It is rare for Israeli soldiers or policemen to be convicted for killing Palestinians.
The Israeli army was unable at the time of publication to give figures for previous such cases.
In 2005, a former Israeli soldier was jailed for eight years over the death of British peace activist Tom Hurndall.