Yet under the 1985 agreement, it has continued to receive aid approximately equal to what it was getting before from the EU’s regional fund. Last year, the EU contributed around 7 per cent of Greenland’s budget (or around €40m.), while Denmark provided another 60 per cent, and the balance was raised by the Greenlanders themselves.

The main source of EU finance has been money paid, under a fisheries agreement (due to run out at the end of 2006), for the right of EU vessels to fish in Greenlandic waters and to help to restructure the Greenlandic fishing fleet. This arrangement recently fell foul of the EU Court of Auditors, who pronounced that the Union was paying far too much for the minimal amount of fish caught.

The Court’s criticisms were backed up by the European Parliament, and the Commission resolved to seek a new basis for the Union’s relations with the Danish dependency. Late last year it set up a task force, under the senior Luxembourg official Etienne Reuter, who had previously represented the EU in Hong Kong and Japan, to thrash out new proposals.

This could be a good time to reopen the question with the Greenlanders. Ever since 1983 its government has been dominated by the left-wing Siumit party, which had led the campaign for withdrawal. In elections last November, the governing coalition lost ground, and though the Siumit leader, Hans Enoksen, remains Prime Minister, the centre-right Atassut party, which was pro-EU, has since been brought into the government.

It is unlikely that the Greenlanders will want to re-run the referendum, at least in the immediate future, but they may now be more open to a new, and possibly closer, relationship with the Union. At the very least, they will want to ensure that a firmer basis is reached for the payment of EU money.

In an interview in his office, Reuter spelled out to me what was in it for the EU. It’s not a matter of charity, he explained; it is in the EU’s self-interest to re-shape its relations with its northern neighbour. There were several fields in which the EU, as well as Greenland, could benefit from closer co-operation.

One of these was geo-strategic. Greenland provided part of the ‘missile shield’ for Western Europe, through the Thule radar base (the largest in the world), leased to the United States, and staffed by Americans and Danes. The EU Galileo satellite system might well be able to use Thule.

Then there was the EU’s interest in managing North Atlantic fishing in an ecological way, while Greenland constituted an excellent laboratory for scientific research in climate change, a vital interest for Europe.

Greenland also had an excellent potential for the development of energy sources, including hydro-electricity, while under the ice cap and the Arctic Sea there may well be extensive mineral resources, as yet untouched.

It is still early days: the task force, which will report directly to the Secretary-General, and is working in close co-operation with around a dozen different directorates-general, is likely to take several months at least before coming up with a draft proposal. This is unlikely to take the form of a treaty, which would require ratification by all the member states.

It would, however, clearly have to be acceptable to the Danish government, which will find itself on both sides of the negotiating table, when the talks start with the Greenlandic authorities, who do not enjoy sovereignty.

This is much to the chagrin of many Greenlanders, who are (at least in theory) in favour of independence, though they are only too aware of their financial dependence on the Danes.

Copenhagen has granted a large measure of autonomy to the Greenlandic government and Parliament, based at Nuuk (formerly Godthåb), a town of 4,000 inhabitants on the south west coast. It has, however, retained control of monetary affairs, foreign and defence policy and justice and immigration.

So, the road to reaching an agreement may not be too smooth, but it is so obviously in the interest of both sides to set the relationship on a new and former footing that it is very much to be hoped that common sense will prevail.

Dick Leonard is author of The Economist Guide to the European Union.