DUP Deputy Leader Peter Robinson has described as 'absolutely outrageous' the appointment of Monica McWilliams as Chief Commissioner of the Northern Ireland Human Rights Commission.
Mr Robinson was speaking in the House of Commons in Westminster.
The DUP's Ian Paisley Junior also claimed the former Women's Coalition MLA was hostile towards his party and could not command the support of unionists.
Professor McWilliams has rejected the DUP criticism.
Her appointment was welcomed by the SDLP and Alliance parties and by the human rights group, Committee on the Administration of Justice. The Irish and British governments also backed her appointment.
Bill of Rights a priority
Earlier Ms McWilliams said her priority for her three-year term would be the introduction of a Bill of Rights.
Ms McWilliams was a founder member of the Women's Coalition party, the group that threatened to break the political mould at the time of the Good Friday Agreement in 1998.
But she and the party's other MLA, Jane Morris, both lost their seats in the 2003 Assembly election and Ms McWilliams went back to a job as a college lecturer.
Some unionists were often uncomfortable with the presence and the policies of the Women's Coalition party.
Many also alluded to the fact that Ms McWilliams, who is from Co Derry, was a first cousin of former Taoiseach Charles Haughey.
The new appointment will bring her back into the public spotlight.
Seven others were also named by the Northern Secretary, Peter Hain, as members of the commission.
