The rupee strengthened 15 paise to 64.39 against the dollar today, backed up by record-shattering stocks, as foreign capital stayed on an upward trajectory. The level of dollar selling by exporters and banks intensified, too. A muted show by the greenback against other currencies overseas added momentum to the rupee. The flagship Sensex broke through the 32,000-mark for the first time ever, which gave the uptrend more lift, traders added. The Nifty too hit a fresh life high. Yesterday, the rupee had recovered 5 paise to close at 64.54 against the US currency. Meanwhile, the benchmark BSE Sensex climbed 215.60 points, or 0.67 per cent, to trade above the key 32,000-mark at 32,020.42 in early session today.