On Thursday, the domestic unit appreciated by 11 paise to settle at 71.45 against the dollar.
The rupee strengthened by 13 paise - or 0.2 per cent - to 71.32 against the dollar in early trade on Friday, a day after the Reserve Bank of India (RBI) surprisingly cut the key interest rate.
The policy action by the RBI amid easing of crude oil rates supported the rupee, say analysts.
On Thursday, the rupee moved 11 paise higher to settle at 71.45 against the dollar.
However, it has depreciated about 2.4 per cent against the greenback so far this calendar year.