The Indian rupee strengthened against the U.S. dollar on Friday, appreciating for the fifth straight session.The local currency opened at 81.27 against the greenback, strengthening 28 paise, or 0.34%, against Thursday's close of 81.55. The rupee depreciated 0.26%, or 21 paise, to end at 81.34 on Friday.The rupee had strengthened throughout the week, gaining 137 paise from the previous Friday's close of 82.72.