The rupee had ended one paisa down at 61.92 against the Greenback on Thursday.
Dollar selling was so strong that even a weak trend in local equities and a firm dollar overseas could not stem the rupee's rise, forex dealers said.
At the Interbank Foreign Exchange market, the domestic unit commenced higher at 61.80 a dollar from previous close of 61.92.
It was trapped in a narrow range of 61.75 -- almost two-week intra-day low -- and 61.90 before concluding at 61.77, logging a rise of 15 paise or 0.24 per cent.
This was its strongest close since 61.76 on November 21. In the previous two sessions, the rupee had softened by four paise or 0.06 per cent.
The local currency also took cues from government's 5 per cent stake sale in SAIL, for an estimated Rs 1,700 crore, generating a robust demand among investors with the offer getting subscribed more than two times on Friday.
The Indian stock benchmark S&P BSE Sensex, however, fell back by 104.72 points, or 0.37 per cent. FPIs/FIIs had injected $103.13 million on Thursday as per Sebi data.
The dollar index, an indicator of other six major global rivals, was up by 0.27 per cent.
Raghuram Rajan: A lucky mascot for the rupee
What is the correct value of the rupee?
Rupee ends nearly flat at 61.92 against dollar
Weakening rupee a sign of volatility ahead
Rupee snaps 2-day climb to end at 61.91 against the dollar