The bosses of academy trusts running large chains of schools in England are going to be challenged by education ministers over "fat-cat" pay.
Lord Agnew says the government's school funding agency is to write to multi-academy trusts asking how pay over £150,000 relates to school performance.
The chief executive of Harris Federation became the first in the state sector to earn over £500,000.
Head teachers say the public needs to be "reassured" over school spending.
Lord Agnew, in a letter to academy trusts, has warned that the funding agency would soon be contacting multi-academy trusts paying above £150,000 - and that if performance is going down, pay for chief executives should also be cut.
Pay cut for low performance
The education minister says that pay for academy bosses should not increase faster than the pay award for teachers.
"I believe that not all boards are being rigorous enough on this issue," writes Lord Agnew.
"My view is that we should see a reduction in CEO pay where the educational performance of the schools in the trust declines over several years."
Schools have protested about worsening funding shortages, and Lord Agnew says academies must show they "deliver the best value for money".
"This is particularly important when looking at the pay of your senior leadership teams."
Education ministers gave tough warnings to universities paying vice-chancellors more than £150,000 per year and threatened intervention over excessive pay.
But more than 120 academy trusts have been paying at least one member of staff more than this - and some many more.
At Harris Federation there were 10 staff earning above the £150,000 threshold, including chief executive Sir Dan Moynihan's pay package of up to £500,000.
The trust says that the pay reflects high performance, with Harris operating 44 schools - all rated by Ofsted as either outstanding or good.
Before Christmas, the Department for Education said it would be raising concerns about pay with academy trusts - but wrote to only small, one-school trusts, rather than large academy chains.
It is now going to contact the big multi-academy trusts.
Paul Whiteman, general secretary of the National Association of Head Teachers, has called for a more transparent pay framework for all staff working the state school sector.
"It is crucial that we set a national framework that defines the roles and sets out the pay and conditions of all those employed in our national, publicly funded education system.
"The public have a right to be reassured that public funds are being used well."
But he warned against creating "an exaggerated debate about leadership pay" and a focus on a "very few high salaries that are not representative of the sector".
The Education Funding and Skills Funding Agency will now write to multi-academy trusts.
A Department for Education spokeswoman said the letter from Lord Agnew "recognises the vital role that chairs of academy trusts play, and will ensure we can continue to work with multi-academy trusts to improve standards for all children, wherever they are growing up".