The title of "headteacher" is outdated and should be replaced by "principal" to allow people who have not qualified as teachers to run schools, the Association of School and College Leaders has said.
The association, which represents about 13,000 secondary heads and senior management team members in Britain, made the recommendation in a submission to consultants PricewaterhouseCoopers, which is carrying out a review of school leadership for the Government.
John Dunford, general secretary, said secondaries should consider the change so that bursars or those with a business background could become the main leader. The title of principal is already used by most colleges, many academies and some schools.
"What is important is whether a person is a good school leader, not whether he or she is a qualified teacher," Mr Dunford said. "We are very definitely not saying that business leaders can be parachuted in to lead schools, but that people with the right leadership qualities and experience should be eligible for the top job.
"The days of the autocratic hero-head are gone, but the days of heroic leadership teams are very much here."
ASCL has recommended that all members of school leadership teams, including senior support staff, should be placed on the same leadership pay scale as teachers. It has also called for incentives so that headteachers stay at the same school for at least five years and generous exit packages for heads who take on jobs at high-risk schools. It proposes that every head should have a sabbatical after five years.
Classroom unions and the National Association of Head Teachers rejected the proposal that principals should not need qualified teacher status.
John Bangs, head of education for the National Union of Teachers, said:
"You have to wonder if ASCL has taken leave of its senses. The title headteacher may seem old-fashioned, but heads should be professional leaders of their schools, and the only way they can command the respect of their staff and their pupils is if they are teachers."
However, the proposal was supported by Valerie Hopkins, who became one of Britain's first school business managers 12 years ago when she was appointed by Stratford-upon-Avon high school, Warwickshire.
Mrs Hopkins, who previously worked for Rolls-Royce, said she was glad that her counterparts in other schools might become principals. "I'm probably too old for it now myself, but if this had happened 10 years ago I would have been enthusiastic," she said. "It is possible to understand education without qualified teacher status".
PricewaterhouseCoopers' report will be published in December