The Swiss government should fill the vacancy at the central bank left by Philipp Hildebrand's resignation quickly rather than waiting until April or May, a member of the bank's supervisory council said on Thursday.

Hildebrand was forced to step down as Swiss National Bank chairman on Monday, after emails cast doubt on his earlier claims not to have known about a big dollar trade made by his wife weeks before he imposed a cap on the soaring Swiss franc.

Finance Minister Eveline Widmer-Schlumpf said on Wednesday the process of finding a successor could take until May. The government makes the appointment based on the recommendation of the bank council, the SNB's supervisory body.

I cannot imagine that we can wait that long, Gerold Buehrer, a member of the bank council who also heads the lobby group economiessuisse, told Swiss television news.

The remaining two governing board members -- Vice Chairman Thomas Jordan and Jean-Pierre Danthine -- were up to the job, he said: I'm firmly convinced that there won't be any lack of security about monetary policy.

Nevertheless, the government should not take too long to appoint a third board member. Since the uproar emerged earlier this month, the Swiss franc has been inching up against the euro, towards the cap set at 1.20. Some in the market say Hildebrand's departure and the absence of a permanent head makes the SNB seem easier to take on.

Emails between Hildebrand, his wife and their banker showed Hildebrand had been involved in discussions on a dollar trade but left it unclear whether he had approved it. That threw into question his earlier statements that he had not known at all about the deal beforehand.

Buehrer said the revelations left little options for Hildebrand but to step down: In the interest of the national bank, I think, the most recent documents made resigning unavoidable.

Speaking at an event in Geneva, meanwhile, Widmer-Schlumpf said efforts were underway to calm the waters roiled by the scandal. Yet she declined to discuss what sort of candidate might be appointed.

We have a team which is working and has the responsibility to continue and to find its way, consolidate the situation, calm down the situation, take care of SNB confidence, that's its work now, she said in response to a question about the process for selecting Hildebrand's successor.

A new permanent chairman and the third board member will likely be named at the same time. Jordan is widely seen as a top candidate to head the SNB permanently.

Hildebrand will receive a year's salary, the SNB confirmed on Thursday, six months to cover his notice period and another six months for a so-called 'cooling' off period.

He received total compensation of 862,000 Swiss francs in 2010, making him the world's highest-paid major central banker.

SNB rules impose a six month ban on Hildebrand, a former hedge fund manager, working for any bank and a 12 month prohibition on his working for a big bank in Switzerland.

Widmer-Schlumpf declined to discuss what Hildebrand might do in the future, but said he had been a very good president of the SNB.

Widmer-Schlumpf was regarded as an ally of Hildebrand's, and has been criticised for standing by the then-governor for too long last week.

I can't tell you what Mr. Hildebrand will do afterwards. I can't tell you where he is. We had good team work, but didn't see each other every day, she said.

(Additional reporting by Catherine Bosley in Zurich; writing by Catherine Bosley)