Mill Hill County High, which went grant-maintained two years ago, is considering selecting up to half of its intake.
Just eight months ago Education Secretary Gillian Shephard gave Queen Elizabeth Boys in Barnet permission to introduce selection.
The 421-year-old school, which was at the centre of a Government inquiry into allegations that it banned troublemakers and low achievers, became only the second GM school to gain Government approval to return to wholesale selection. From last September it was allowed to admit 160 boys a year on academic standards and 20 for their musical ability.
Mill Hill County's proposals will not be published until next week but it is understood to be looking at selecting 30 per cent of pupils on technology and mathematical grounds with tests comprising non-verbal reasoning, maths, an essay and practical investigation.
The mixed 11-18 school with 1,242 pupils, has already modified its admissions criteria to take in up to 10 per cent of pupils on musical ability. It is now considering extending that limit to 20 per cent to cater for pupils with either musical or dance talents.
Pupils awarded places on musical merit will have to submit copies of certificates and dancers expected to demonstrate achievement. All applicants and their parents will be interviewed "as a means of ensuring that all parties are aware of the ethos and character of the school" according to a consultation paper.
The school has a high academic reputation. It has regularly sent students to Oxford and Cambridge and for the past two years 45 per cent of A-level passes have been at grades A and B.
Its proposals have already upset local parents who claim that seven of the 10 GM schools in Barnet are already selective - six on religious grounds. They fear that the remaining three opt-outs will be now forced to go down the selection route. They have also criticised the consultation process.
Jenny Brown, secretary of Barnet Parents, said: "People are very worried about us returning to the old 11-plus and the secondary moderns. When Mill Hill went grant-maintained there wasn't any indication that it was going selective. In fact, the opposite."
Louise James, Mill Hill County deputy head, said the principle reason for the technological and mathematical selection was to enhance the school's technology base.
Hendon Boys GM school in Barnet is also considering changes in its admissions criteria.
The 950-pupil school wants to introduce banding from September 1996 with all pupils sitting a standardised national test with the top 25 per cent being awarded 50 places, the middle 50 per cent 100 places and the lowest 25 per cent, 50 places.
Robert Lloyd, headteacher, said: "The whole point of changing our criteria is not to become selective but to ensure us remaining as a comprehensive school. "