* Dollar rebounds after Fed meeting * Euro falls 0.5% against the dollar, 0.3% against CHF * BoE unexpectedly keeps rates on hold, sterling falls 0.8% * Norway’s central plans to raise rates next month LONDON, Nov 4 (Reuters) - The dollar rebounded on Thursday, recovering after the Federal Reserve repeated it saw high inflation as transitory, while sterling dropped after the Bank of England unexpectedly kept interest rates on hold. The Fed announced on Wednesday a $15 billion monthly cut to its $120 billion in monthly purchases of Treasuries and mortgage-backed securities, but Chairman Jerome Powell said he was in no rush to hike borrowing costs. The move was initially seen as favourable to risky assets, with Wall Street indexes closing at record highs while the safe-haven dollar fell sharply against a basket of major currencies. Gradually, however, investors took a more balanced view of the Fed monetary policy update and the overall picture painted by fresh upbeat data for the U.S. services industry. The dollar index swung back from a low of 93.80 points shortly after the Fed announcement on Wednesday to 94.319 around 1200 GMT on Thursday, its highest since October 13. “I think most people would have been looking for a dip to buy dollar,” said Kit Jukes, a macro strategist at Societe Generale. The euro, he noted, remained under pressure against the dollar with the European Central Bank seemingly far behind the Fed in tightening. ECB President Christine Lagarde on Wednesday pushed back on market bets for a rate hike as soon as next October and said it was very unlikely such a move would occur in 2022. The euro fell against the dollar on Thursday, down 0.5% at $1.1554 and also briefly hit its lowest level against the Swiss Franc in 18 months at 1.053 franc per euro. Sterling, which had initially led the gains on the dollar after the Fed move, sustained its heaviest losses against the dollar since September after the Bank of England took investors by surprise and kept interest rate on hold. Markets were expecting it to become the first major central bank to raise rates since the COVID-19 crisis. At 1221 GMT, sterling was down about 1% against the dollar at $1.3552 and down 0.5% against the euro at 85.23 pence. “It was a surprise for sure and it looks like they got a bit nervous and have turned to data dependency, which keeps every meeting live going forward”, commented James Rossiter, senior global strategist at TD Securities. While markets were pricing in a rate rise from the BoE, economists polled by Reuters said the move was too close to call, as Britain, like much of the world, seeks to balance its fight against inflation without compromising the economic recovery. Elsewhere in Europe, Norway’s central bank said, as analysts expected, that it planned to raise its key policy interest rate next month, continuing a campaign of monetary tightening that started in September. The crown ticked slightly higher to 9.87 against the euro . In the last three months, the crown has strengthened by about 7% against the euro. The yen was flat with one dollar at 114 yen within a good leap of the dollar’s multiyear high of 114.69 yen hit last month. The Aussie dollar lost 0.44% at $0.7413, close to the levels it fell to on Tuesday after the Reserve Bank of Australia adopted a dovish tone at its key meeting. In the world of cryptocurrencies, bitcoin was down about 2% at $61,631 having largely traded sideways since it hit its all-time high of $67,000 last month. Reporting by Julien Ponthus, Dhara Ranasinghe and Alun John; Editing by Gerry Doyle, William Mallard, William Maclean