Traders said the franc's initial push higher against the euro on the announcement had run out of steam and failed to seriously test the 1.20 francs-per-euro cap that Hildebrand had imposed in early September, leading to the controversy that cost him his job.

"The 1.20 level could come under pressure but I wouldn't get too excited. There's some movement in the euro-dollar but in other currency pairs trading is light, the year hasn't really started yet," said one Zurich-based currency trader.

In early Tuesday trading the franc lost some of the ground gained against the euro in the aftermath of Hildebrand's resignation as traders mooted there would be no central bank policy change under interim SNB chairman Thomas Jordan.

"At this stage we see little room for the SNB to take a step back from their current monetary policy and hence expect them to stay committed to the lower boundary in EURCHF at 1.20 for some time to come," said UBS economist Reto Huenerwadel in a note.

The franc remained firmly in the 1.21-1.22 francs per euro range in which it has traded since the start of the year after failing to breach the 1.21 level earlier in the session, falling 0.1 percent compared to the new York close to trade at 1.2124 francs per euro at 0848 GMT.

The franc was flat against the dollar compared to the New York close at 0.9496 francs per dollar. Against the euro, the franc dipped 0.1 percent to trade at 1.2125 francs.

Some observers said traders could yet look to gauge the willingness of interim SNB chief Thomas Jordan to defend a weaker franc in the near term now that the man seen as the architect of the franc-euro is out of the way.

"Jordan is a good man but relatively new in the job, and it remains to be seen whether the markets will want to test his resolve on the franc early. The next 48 hours will be critical," said IMD Business School professor Stephane Garelli.