THE council excluded backbench councillors from the decision to appoint VT Education and Skills (VTES) to run some of its education services, it has been claimed.
VTES was picked ahead of other bidders during the selection process late last year.
A "stakeholders" panel was set up, which included three councillors, a number of school governors and education representatives to scrutinise each bid.
But the three councillors, Liberal Democrat James O'Rourke, Labour's Adam Gladstone, and the Conservative's Marion Fitzgerald quit the panel, unhappy about the way the process was conducted.
Cllr Fitzgerald said: "We were not happy when we realised that the so-called stakeholders panel would not have any direct responsibility and would not be interviewing any of the applicants."
Cllr Fitzgerald said that different members of the panel would see different parts of the bids, so that members would be expected to vote without getting the full picture.
She also said that the overall vote by the panel would have only a small effect on the overall decision in any case.
She said: "Backbench councillors from all parties have therefore been excluded from meaningful active participation in this appointment."
After the members left the panel, the council's executive director for children and young people, Chris Kearnan, said that he was not concerned as councillors were not "stakeholders", an attitude described by Cllr Fitzgerald as "absurd".
At last Thursday's full council, education cabinet member Chris Robbins said he thought that involvement of backbenchers had been "thorough and extensive".
He said: "Cllr Fitzgerald is quite mistaken in saying that the council took the attitude that councillors should not be consulted, alongside stakeholders, as part of the procurement process for the new school improvement contract.
"The members who were included in the consultation, despite not being stakeholders as such, chose to be excluded, and wrote to the director expressing their reasons for this."
From April 1, VTES will take over some of the services currently provided by EduAction, including school improvement, admissions and pupil and student award functions.
It will also provide support to schools involved in the Government's Building Schools for the Future programme, which will eventually see every secondary school in the UK rebuilt or refurbished, mainly through the use of public-private partnerships.
VTES is part of the VT Group, which is one of the world's leading suppliers of military products.
The council's decision to choose an arms company to manage education has been criticised by some teachers and unions.
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