Mr Thyne, who is 54, has been head of Fettes for 10 years. The school is at its maximum capacity of 500 pupils who pay an average Pounds 12,500 a year.
"Unprecedented" publicity for Fettes as the Prime Minister's former school has helped recruitment, Mr Thyne says. He gives good marks to Tony Blair for the Government's emphasis on education, especially on standards and methods of teaching. There has been recognition "that whole-class rigorous teaching is of fundamental importance".
But he deplores the decision to end the assisted places scheme. Although the school's own resources will continue to support some who cannot afford to pay full fees, the number is bound to drop.
In the phasing out of assisted places, Fettes, which has 40, will lose six or seven low-income pupils a year. "Unlike some schools, our governors made sure that we were not financially overexposed to what was recognised as a politically fragile scheme," Mr Thyne says.
Fettes is about to embark on a seven-year business plan that will involve raising substantial sums to build a new sports centre and enhance cultural facilities, and Mr Thyne believes a new head with "fresh energy and ideas" should take charge of the developments.