If the plan they come up with does not satisfy Rosemary Butler, the Welsh Assembly's education secretary, then the school could become the first in Wales to be handed over to an education association or closed and given a "fresh start".
Neither of these drastic options has yet been used in Wales, which currently has only three other schools and one pupil-referral unit under special measures.
The inspection in April found low standards of achievement, poor discipline and high levels of truancy at Glan Ely high.
The school had failed an earlier inspection and was put under special measures from 1995 to 1997, but it was subsequently released fom them because it appeared to have improved.
This latest inspection found that the improvement had not been sustained and had not had enough impact on pupils' achievement.
The "naming and shaming" of Glan Ely was criticised by staff and governors, who said Estyn, the Welsh inspectorate, had failed to take into account the poor socio-economic conditions in which the school operated.
Gethin Lewis, head of NUT Cymru, said Estyn's "harsh subjective judgment", based on a comparison of the school's results with national averages, was unfair and damaging.
But Estyn said its inspections always took full account of a school's circumstances and stressed that many schools in areas of disadvantage were very successful.
The inspectorate is now working closely with Cardiff county council on the action plan for the school.