The Sensex opened higher at 20,755.73 and firmed up further to 20,778.13 on initial buying mainly in metal, power and refinery sector stocks.
It, however, declined afterwards to 20,669.80 before quoting at 20,710.23 at 1030 hours, showing a loss of 19.15 points or 0.09 percent from its last close.
The NSE 50-share Nifty also moved down by 8.20 points or 0.13 per cent to 6,166.40 at 1030 hours.
Key benchmark indices in Hong Kong, Singapore, Taiwan, South Korea and Japan were down 0.06 per cent to 1.23 per cent, while those in China and Indonesia were up 0.25 per cent to 0.36 per cent.
Fed's bond-buying programme has been a source of liquidity for most Asian and emerging markets over the past few years.
Meanwhile, foreign institutional investors (FIIs) bought shares worth a net Rs 79.68 crore yesterday as per provisional data from the stock exchanges.