Published Wednesday, 15 February 2012
The portrait by Lydia de Burgh has been moved to Hillsborough. (© UTV)
Mr Allister was talking specifically about a table on which the Act of the Union was signed on in 1800, which is currently being held in storage.
Meanwhile a portrait of the Queen by the Irish painter Lydia de Burgh, which used to hang in Parliament Buildings, is now at Hillsborough Castle.
The North Antrim MLA wants the items put back on display.
"Under the current regime there has been a sanitising of Stormont of any artefact which tends towards support of the union," Mr Allister told UTV.
"Notable in that is, for example, the table which the Act of Union was signed upon which used to stand in this hall and a portrait of Her Majesty, a very beautiful portrait by the artist de Burgh, which has been removed.
"Now of course we are into the diamond jubilee and it seems a very appropriate time to ask how we can celebrate if the primary building in Northern Ireland, Parliament Buildings, is cleansed of every last portrait of her."
In a statement, the NI Assembly told UTV a number of items were removed in 1995.
It said: "Following a serious fire in Parliament Buildings in late 1995, a full refurbishment programme was undertaken.
"This involved the removal of a number of artefacts, to long term storage, in advance of a re-painting and renovation programme over the period 1996 - 1998.
"Any future display of artefacts and memorabilia will be a matter for the Assembly Commission to consider, in discussion with the Political Parties and consistent with Section 75 (2) of the Northern Ireland Act 1998 Good Relations duties."