Details of the meeting, and the school, will be made public. Mr Byers said the Government is determined to make sure that no school drifts into long-term failure as he announced new measures to speed the post-inspection process up.
Schools under special measures are to have their follow-up inspection six months after the original inspection, rather than 12-18 months later as at present.
If after four terms the school is still not improving, there will be a "case conference" with the Office for Standards in Education. If there is still no evidence of change the next term, the head, chair of governors, and local authority representative will be called to meet ministers. The meeting would be made public because "children only get one chance of education", Mr Byers said.
The move was announced as Mr Byers defended the Government's "name and shame" policy in a debate with David Hart, general secretary of the National Association of Head Teachers, at the London Institute of Education this week.
David Hart had argued that 17 out of the 18 heads at the named and shamed schools believed the policy was damaging and had not contributed to improvement. He asked why the teaching profession is singled out for public opprobrium: "The Secretary of State for Health doesn't plan to summon doctors or surgeons, the Lord Chancellor does not summon solicitors or barristers I dragging teachers through the streets like this is going a bit far."
He also asked why Mr Byers felt that further measures to identify failure publicly were necessary when the Government already had a "formidable package" of existing powers and more were planned in the forthcoming Bill.
Mr Byers said: "These schools had been in special measures for a total of 346 months between them; they had had 49 inspections and were responsible for 7,900 pupils ... I would have been failing in my responsibility to those pupils if I turned my back on them." He emphasised the public's right to know what is going on in schools and made no apology for publishing this information via the media.
Mr Byers faced a largely hostile audience which included three heads of named and shamed schools. Greta Akpeneye, former head of Lilian Bayliss school in Lambeth, said OFSTED had found the school to be improving long before it was included on the list. "Tell your lackeys to learn to read," she told Mr Byers angrily, saying that her pupils had assumed that they were "rubbish" after the school had been named.
Mr Byers praised Sarah Briggs, the pupil who was suspended and then reinstated after exposing problems at Queen Elizabeth School in Nottinghamshire. "Sarah Briggs challenged the establishment, who didn't want publicity I I'm pleased the head has now resigned," he said.