* Dollar index hovers near its highest level since Dec. 20

* Yen gets some respite from selloff

* Dollar comes off previous day's 5-year high vs yen

By Masayuki Kitano

SINGAPORE, Jan 3 (Reuters) - The dollar held steady near a two-week high versus a basket of currencies on Friday after positive U.S. economic data reinforced expectations the Federal Reserve will continue to step away from its bond buying stimulus.

U.S. factory activity held near a 2-1/2-year high in December and the number of Americans filing new claims for jobless benefits fell again last week, data showed on Thursday, suggesting the world's largest economy was on stable footing.

Against a backdrop of a firming jobs market and brightening economic outlook, the Fed said in December it would reduce its monthly $85 billion bond buying program by $10 billion starting in January.

The dollar index, a gauge of the greenback's value against six major currencies, last stood at 80.607, having risen to as high as 80.709 on Thursday, its strongest level since Dec. 20.

Market participants said Thursday's moves had been exacerbated by thin market conditions at the start of a new year.

"There is a severe shortage of liquidity, with Tokyo on holiday...and the mid-week New York break meaning many participants are not at their desks this week," said Jeffrey Halley, FX trader for Saxo Capital Markets in Singapore.

Against the yen, the dollar last fetched 104.80 yen, steady from late U.S. trade on Thursday but down from a five-year high of 105.45 yen set on Thursday on trading platform EBS.

The yen also gained some respite versus the euro, which eased 0.1 percent to 143.15 yen, following a 1.2 percent drop on Thursday. The common currency has backed off from a five-year high of 145.67 yen set last Friday.

"Many people are long the dollar versus the yen and cross/yen pairs in thin market conditions, after the market tested the upside a bit excessively toward the end of last year," said Satoshi Okagawa, senior global markets analyst for Sumitomo Mitsui Banking Corporation in Singapore.

Thursday's falls in the dollar and the euro versus the yen were likely caused by position squaring in thin liquidity, Okagawa added.

Against the dollar, the euro eased 0.1 percent to $1.3658 , staying within sight of a two-week low of about $1.3630 set on Thursday.

The drop in the euro came in the wake of its rise to a two-year high of $1.3894 last Friday.

The euro had risen in thin trading conditions in late December, supported by factors such as euro zone banks repatriating funds to shore up their capital bases before an asset quality review by the European Central Bank.

The Australian dollar eased 0.2 percent to $0.8894 and touched an intraday low of $0.8886 after a survey pointed to a slowdown in the services sector in China, Australia's top export market.

China's official purchasing managers' index for the non-manufacturing sector dipped to 54.6 in December from 56.0 the previous month, mirroring a slowdown in manufacturing activity growth.