Two sisters beheaded their own uncle and his wife in front of the couple’s children because the man wore Western-style trousers, according to Iraqi police.
The suspected al-Qa’eda militants told investigators that Youssef al-Hayali was an infidel because he did not pray and wear appropriate clothing.
He was executed along with his wife Zeinab Kamel at the school in Diyala province northwest of Baghdad where Mr Hayali worked as a security guard.
Some Sunni Arab communities across Iraq have been turning against al-Qa’eda fighters because of its indiscriminate killings.
Sunni Arab tribal sheikhs have been organising their young men into neighbourhood police units to drive out the militants.
US and Iraqi officials say has helped bring down violence levels across Iraq.
Security operations by US and Iraqi troops have also been targeting al-Qa’eda in ethnically and religiously mixed Diyala in recent months after Sunni Islamist fighters were driven out of western Anbar province.
The US military said earlier this month that it was sending 3,000 soldiers home from the province but added that the overall number of forces in the province would not decrease.
The United States sent an extra “surge” of 30,000 troops into Iraq in February in an attempt to stop the country from sliding further into sectarian civil war.