The Rupee on Tuesday saw a subdued start with a loss of just one paise at 64.45 against the US Dollar.
Strength in the Dollar against other currencies overseas made the Rupee keep a low profile.
Traders attributed the Rupee's fall to increased demand for the US currency from importers and banks and a lower opening in the domestic equity market.
On 12 June, the Rupee was down 20 paise to end at a one- week low of 64.44 amid concerns about a probable Fed rate increase.
Meanwhile, the benchmark BSE Sensex fell 19.90 points, or 0.06 per cent, to 31,075.80 in opening trade on Tuesday.