Seymour Major, a prolific Tory party blogger, has started a campaign for a separate organisation with a new name and would seek to align with the Conservatives at Westminster, but remain agnostic on the Union. The contention is that unionism has become toxic in Northern Ireland and the Tories at national level are indelibly linked to it. This breed of local Conservative doesn't just want to keep the UUP at arm's length, they feel the same about David Cameron.
Their difficulty is that any new party would start with an even smaller base than the Northern Ireland Tories.
In a devolved UK, constitutional issues are part of everyday debate and, by ducking the border issue entirely, a neutral centre-right group here could not offer either equal citizenship or normal politics.
But there is a strong alternative view, which argues that the existing party should press ahead with its Conservative and Unionist branding - with or without the UUP.
The New Force tag should be dropped and much of the baggage for which UCUNF was ridiculed could be shed with it.
By embracing this approach the Northern Ireland Conservatives would also be ideally placed to attract disillusioned Ulster Unionists, if the UUP decides to go down the 'unionist unity' route.
Indeed, the Northern Ireland Tories could emerge strengthened from a realignment in unionism.
Stiff resistance within the UUP to any DUP link is likely and there remains an influential section of the party convinced that the Conservative pact was a positive strategy.
Indeed, a Northern Ireland Conservative and Unionist party would make a natural vehicle for secular unionism, without Orange trappings and an ideal partner for David Cameron's Government.
If the local Tories instead decide that having a view on the province's constitutional future can be equated with sectarianism, they will quickly return to relative obscurity.