A STORM has broken on the far right of Italian politics. Gianfranco Fini, Italy's deputy prime minister and leader of the National Alliance, first whipped it up last month, when he said he wanted all legal immigrants to be given the vote in local elections. Then came a visit to Israel, during which he disowned much of his movement's chequered past and pointed it down a road that might lead to international conservative respectability.

The National Alliance was founded in 1994 as a broadly based successor to the Italian Social Movement (MSI), created after the second world war to keep alive the ideals of Benito Mussolini. Yet in Israel, Mr Fini denounced Mussolini's anti-Jewish laws as “disgraceful” and said that fascism was an “absolute evil”. On his return, he went further still, declaring that anti-fascism was a core value of his party.

This was too much for the dictator's grand-daughter, Alessandra Mussolini, who said she was resigning from the National Alliance to form a movement of her own. She was not alone in her disgust. Far-right fans of the Turin soccer club, Juventus, unfurled a banner that read “Fini: betrayer of Italy”. Yet pollsters say the anti-Fini brigade is in the minority. A survey for the Corriere della Sera found that only 3% of National Alliance voters felt that Mr Fini had taken a wrong turn in Israel. As many as 58% saw themselves as belonging to the “centre-right”, or even “centre”.

Ms Mussolini has a hard row to hoe. The creation of the National Alliance spawned an earlier rejectionist party, led by a former MSI notable, Pino Rauti, that went nowhere. But Mr Fini is also taking a risk, which could grow if weightier figures than Ms Mussolini were to defect, as some are threatening. Any loss of the party's core support could undermine his entire claim to leadership.

However, if Mr Fini pulls off his attempt to disown the party's fascist roots, he could win a glittering prize. The right won a stunning victory at the 2001 election. It has a big enough majority to ram through such controversial measures as a new media law, passed this week, that seems designed to benefit the TV empire of Silvio Berlusconi, the prime minister and leader of Forza Italia. Yet the right is fragile. If Mr Berlusconi goes, Forza Italia could fall apart, with little left to take its place. The conservative wing of the old Christian Democrat party is too small, and Umberto Bossi's xenophobic Northern League both too regionally based and too far from the mainstream.

Distance from the mainstream was long a characteristic of the National Alliance, too—until Mr Fini's visit to Israel. Now it is starting to look more like the Popular Alliance (later Popular Party) that Manuel Fraga fashioned from the wreckage of Francoism in Spain in the late 1970s: a movement that could conceivably link with conservative Christian Democrats to become the dominant party of the right. The PP, under José María Aznar, has governed Spain for almost eight years.