* Euro falls, dollar index hits 2-week high
* Euro zone inflation at four-year low, unemployment high
* Market unwinds dollar shorts after Fed announcement
* Fed keeps stimulus in place, not too alarmed on growth
By Jessica Mortimer
LONDON, Oct 31 (Reuters) - The euro fell to a two-week lowagainst the dollar on Thursday after a fall in inflation to itslowest in nearly four years increased speculation that theEuropean Central Bank will ease monetary policy further.
Helped by the euro's falls, the dollar hit a two-week highagainst a basket of currencies.
The U.S. Federal Reserve sounded somewhat less alarmed aboutthe pace of the economic upturn than some investors had expectedafter a meeting on Wednesday, prodding the dollar higher.
The euro lost 0.7 percent to $1.3638, its lowestsince Oct. 17.
Euro zone flash annual HICP inflation fell to just 0.7percent in October. This may raise concerns among euro zonepolicymakers about deflation risks and damage to the economyfrom a strong currency. Euro zone unemployment was at a recordhigh 12.2 percent.
ECB governing council member Ewald Nowotny said earlier onThursday the central bank would provide more liquidity whencheap long-term loans it made in late 2011 and early 2012expire.
"We have had a nasty combination of a lack of inflationarypressures and record unemployment, and the market'sinterpretation is that the ECB may sit up and take notice," saidJeremy Stretch, head of currency strategy at CIBC.
"The downside risks for euro/dollar look evident and $1.36is a near-term target."
The dollar index rose 0.25 percent to 79.984, itshighest since Oct. 17, as it pulled away from a nine-month lowof 78.998 hit on Friday.
The U.S. central bank dropped a phrase in its statement onWednesday expressing concern about a run-up in borrowing costsand made no direct reference to the partial government shutdownearlier this month.
"The market was expecting a relatively dovish outcome fromthe Fed and that's why we've seen some profit-taking. People hadbecome too bearish on the dollar and too bullish oneuro/dollar," said Arne Lohmann Rasmussen, head of foreignexchange research at Danske Bank.
The dollar fell 0.3 percent against the yen, however, to98.19 yen. Weaker equity markets helped the safe-havenJapanese currency even as three Bank of Japan board membersdissented against the latest semi-annual report, with someciting stronger downside risks to the economy.
The Australian and New Zealand dollars also gained against their U.S. counterpart on strong Australianhousing data and after the Reserve Bank of New Zealandreiterated it was likely to hike interest rates next year.