The charity regulator says independent schools will have to continue to prove their worth to keep claiming charitable status.
A total of 52 schools in Scotland have charitable status which can help them reduce their tax bills.
The regulator has looked at the schools one by one to ensure they were doing enough to justify their status.
Forty met the test and a further 10 did so after they took action to address concerns.
Two reviews were suspended due to particular circumstances.
The details are contained in a report by the Scottish Charity Regulator.
Only about 4% of pupils in Scotland attend private schools. The regulator has been examining whether the schools do enough to justify charitable status - for example, bursaries for those families who cannot afford fees.
Critics have long questioned whether schools which charge most of their students fees should be allowed charitable status.
The regulator's charity test sets the standard that all of Scotland's 23,700 charities must meet in providing public benefit.
There are key tests to qualify as a charity: for example they have to show public benefit from their work and access to their services cannot be unduly restrictive.
The Office of the Scottish Charity Regulator's head of registration, Martin Tyson, said the review demonstrated the role of the regulator in maintaining public confidence in charity law.
He said: "From the commencement of the charity legislation in 2006, we identified fee-charging schools as a priority group that continues to have a high degree of interest from the public.
"Where we have found problems we have taken action to ensure that charities are all now doing what the charity test requires.
"More recently, we embarked on a full-scale review of this group and today's report sets out our findings and key issues."
He added: "Our work is aimed ultimately at reinforcing public confidence and our report illustrates both the issues we consider and the enforcement action we take where required.'
Since 2007 the charity regulator has reviewed the charitable status of 52 independent schools on the charity register.
The actions the 10 charities took to meet the criteria included increasing the support they offered for those unable to pay fees.
Since 2012, five schools failed the charity test: Fettes College, St Columba's School, St George's School for Girls, Wellington School and Loretto School.
The regulator said all of them responded well to its concerns and subsequently passed.
Conservative young people spokeswoman Liz Smith, a former pupil and teacher at the fee-paying George Watson's College in Edinburgh, said: "This report demonstrates the effectiveness of the 2005 charities test legislation which was unanimously agreed by all parties at Holyrood.
"That legislation rightly ensures that there is a very rigorous test for all independent schools to undertake prior to being awarded charitable status."
She added: "The report makes it very clear that the independent schools have been more heavily scrutinised than any other group within Scotland's 22,000 charities and that any concerns about individual schools have been fully addressed prior to the award of charitable status.
"If schools do not meet these criteria, they fail the test.
"That is exactly as it should be and should put an end to those who argue that all independent schools should be stripped of charitable status."