The Scottish Council of Independent Schools (SCIS) has said that 91.4 per cent of pupils taking Highers achieved A to C grades this year, an increase on last year's total of 90.8 per cent.
While no separate pass rate is provided for state schools, the fact that the overall pass rate fell from 77.4 per cent to 77.1 per cent, while private schools' performance improved, shows that the gap between the sectors has widened.
However, the percentage of private school students achieving A grades in their Highers fell for the first time in seven years. In total, 55 per cent of S5 Highers taken in independent schools resulted in A grades, only a small drop on last year's 56 per cent but breaking a cycle of year-on-year improvements dating back to 2007.
The fee-paying St Mary's Music School in Edinburgh achieved a 100 per cent pass rate in S5 Highers, although only a small number of students took the exams.
At the larger private Edinburgh Academy, Mary Erskine School and George Heriot's School, all also in the capital, Higher pass rates of more than 97 per cent were achieved. The three schools all charge upwards of £10,000 per year and students must go through a selection process to be admitted.
While the top four performing private schools are in Edinburgh, St Aloysius' College in Glasgow completed the top five, with a Highers pass rate of 96.2 per cent.
John Edward, SCIS director, said: "In this transition year for qualifications the only meaningful comparison we can make are at Higher and Advanced Higher level, which both show consistently high levels of achievement."
The statistics also showed the "great range and depth of subjects and qualifications open to independent school pupils", Mr Edward said. The number of private pupils achieving an A to C grade in the new National 5 exams reached 93.9 per cent, of the 7,202 entries. The exam has replaced the replaced Standard Grade.
The statistics also revealed 13.6 per cent of private Higher candidates achieved three or more A grades. All of the 176 pupils taking the Scottish Baccalaureate passed.
Overall, almost 15,000 Highers were taken by private school pupils this year, representing 7.6 per cent of the total number across the independent and state sectors.
The picture of a widening attainment gap was repeated for Advanced Highers. While the pass rate exclusively in private schools remained static, at 92.6 per cent, it fell when state schools were included, dropping from 82.1 per cent last year to 81 per cent.
The High School of Glasgow came sixth in a league table of private school Higher pass rates, with 96.1 per cent of entries achieving an A to C grade and students taking five of the qualifications each on average.
Colin Mair, Rector at the High School of Glasgow, said: "Our pupils' performance in the Advanced Highers in sixth year was also excellent, a pass rate of 93 per cent with 58 per cent at Grade A.
"These excellent results complement our pupils' involvement and success in a wide range of extra curricular activities including music, sport, expressive arts, public speaking, community service and the Duke of Edinburgh's awards. We congratulate all our pupils on another very successful year, with the support of their parents and teachers".