The ATGWU and British Midland's ground handling staff have rejected the airline's invitation to go to the Labour Court for talks.
Last week, the company reached an agreement with union representatives on a transfer package following the sale of its ground handling operations to GHI.
It was endorsed by the Labour Relations Commission but rejected by workers.
The package included retention of all employees by GHI, a once-off payment, transfer to GHI's pension scheme, retention of travel concessions and current pay package.
British Midland has expressed regret at the ATGWU's unwillingness to return to talks.
Jill Nealon, Director of Personnel said, "We are naturally disappointed that our offer of further talks through the Labour Court has been rejected by the ATGWU. We have been willing to discuss a means of resolving this dispute through the Labour Court."