About 3, 000 members of Nipsa are staging an indefinite strike over pay and job re-grading.
BBC: NEWS | UK | Northern Ireland | Classroom dispute talks continue
John Corey from the public service union, Nipsa said the proposed changes were "unreasonable and unfair".
BBC: NEWS | UK | Northern Ireland | Strike hits schools and transport
The Northern Ireland Public Service Alliance (NIPSA) union had campaigned for the jobs to be decentralised.
Noel Griffin from NIPSA said some of their members had expressed concerns but others had welcomed the move.
Unions involved in the strike include Nipsa, Siptu, TGWU, ATGWU, Amicus and Unison.
BBC: NEWS | UK | Northern Ireland | Strike hits schools and transport
Speaking on his way into the meeting, Nipsa's John Corey said the employers must be prepared to reach a deal.
BBC: NEWS | UK | Northern Ireland | Classroom dispute talks continue
The deputy general secretary of the trade union Nipsa, Brian Campfield, said jobs could be lost because of the cuts.
BBC: NEWS | UK | Northern Ireland | Board cuts lead to resignations
Janette Murdock from public service union NIPSA, who works in Torbank Special School, said promises of a deal have not been honoured.
BBC: NEWS | UK | Northern Ireland | Class assistants protest pay wait
"We object to the language in the letters and we object to the whole process, " said Kevin McCabe, assistant secretary of Nipsa.
Nipsa general secretary John Corey said strike action was a last resort.
BBC: NEWS | UK | Northern Ireland | One-day strike at special school
He added that NIPSA believed many of the "initial problems" raised by its members could be resolved through its negotiations with the department.
NIPSA's Assistant General Secretary, Kieran Bannon, said the union was not against decentralisation, it just wanted clarification as to why Ballykelly was chosen.
In reply to a question from the UUP's Michael Copeland, the minister outlined the meetings her officials were holding with the NIPSA trade union.
Bumper Graham from Northern Ireland's largest public sector union NIPSA, said many of its members had been hit by salaries not going into their Ulster Bank accounts.
Mr Griffin said some NIPSA members had expressed concerns about their future in the department, but he believed potential difficulties could be resolved through the union negotiations.
John Corey of the public service union Nipsa said the termination of the project was "in the best interests of the civil service and the Northern Ireland taxpayer".
The Royal College of Nursing and the public service union Nipsa have criticised the decision to send a questionnaire to staff at the board and the Public Health Agency who are understood to have had access to the reports.
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