Down have decided to oppose the opening of Croke Park to football and rugby but only on the chairman's casting vote.
The Croke Park issue is expected to dominate the GAA Congress
Wednesday's debate on Rule 42 resulted in delegates evenly split on 20 votes each and chairman Jerry Quinn then opted to oppose any change.
The controversial rule dictates that the GAA's Dublin modern venue should be used for Gaelic games only.
Those favouring change have argued that the close vote indicates a move towards opening up the 80,000-seater stadium.
Reports from the Down meeting suggested clubs wanted a change but found their wishes countered by the management committee.
The eventual outcome means seven of the Ulster counties are expected to oppose any change to the current rule. Donegal and Cavan are the only Ulster counties expected to back a new stance.
There have been calls for the GAA to let the Irish rugby and football teams play at the north Dublin venue while Lansdowne Road is being redeveloped.
If that does not happen, they may have to stage their home international fixtures at a British venue.
Congress votes on the matter on 16 April, with a two-thirds majority needed to pass a motion.
Despite the Ulster opposition, support in other provinces could mean a close-run thing.