The union has claimed that it was not consulted over the redundancies and said that standard redundancy practices were not followed.
Unite said it is now in the process of appealing four of the redundancies, although so far has failed to make contact with the company.
Graham & Heslip went into administration with BDO Stoy Hayward on 2 December, but was sold shortly afterwards to C&R Print, a company set up by G&H managing director Diarmuid McGarry and Adrian Glenn.
However, it has emerged that redundancy procedures began at the company on 20 October, two days before C&R Print was created.
According to Unite, staff were informed at a meeting on 20 October that redundancies would take place, and a letter was later sent out confirming this.
Joanne McWilliams, unite regional officer, told PrintWeek that the letter stated 34-45 redundancies would be made and each department could elect a representative.
She also claimed that it stated: "The proposed method of dismissing employees will be on a last-in, first-out basis."
According to Unite, no further discussions took place until around 20 November, when the company began making staff redundant. Redundancies took place on several days, between 20-23 November.
A letter, also sent out on differing days between 20-23 November, stated: "I refer to our recent discussions regarding company redundancy proposals and, in particular, our discussion today regarding the outcome of the selection process."
McWilliams said that no formal meeting took place and that staff who were dismissed were merely called in to a meeting room and "essentially told 'you're it, see you'".
She added: "I have called regarding the appeals, but as of yet there has been no response."
McGarry was not available for comment at this time.
Clarification: C&R Print of Enniscorthy, County Wexford, Ireland, which was established 1979, is in no way associated with the C&R Print, which has its registered office in Lisburn, County Antrim, Northern Ireland, that purchased the assets of Graham & Heslip.
