The Rupee firmed up 6 paise to 64.68 against the Dollar on Wednesday after increased selling of the US currency by exporters and banks.
It received backing from a weak Dollar against other currencies overseas.
Further, foreign capital inflows and a higher opening in the domestic equity market took the local unit higher, dealers added.
On 4 July, the Rupee had gained 14 paise to close at 64.74 against the greenback on fresh bouts of Dollar selling.
The benchmark BSE Sensex rose by 74.85 points, or 0.23 per cent, to 31,284.64 in opening trade.