The rupee fell by 21 paise to trade at 63.24 against the US dollar on the first trading day of the New Year due to buying of American currency by banks and importers.

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At the Interbank Foreign Exchange, the rupee opened lower by 21 paise against previous close of 63.03. 

Dealers said increased demand for the American unit from importers and a lower opening in the doemstic equity market weighed on the rupee. Dollar's gain against major world currencies also influenced the rupee movement, they added.

The rupee had appreciated by 35 paise to end at two-week high of 63.03 against the greenback on Thursday.

Meanwhile, the benchmark BSE Sensex fell by 83.84 points, or 0.30 per cent, to 27,415.58 in early trade.