The rupee firmed up 4 paise to 64 against the dollar today, taking cues from a higher opening in the domestic stock market. The US currency lost muscle even as the Republican tax cut package moved closer to becoming a law. In the opening session, the domestic unit went up 4 paise to 64 against the dollar. Yesterday, it had gained 20 paise to close at a three-month high of 64.04, building on the momentum after the BJP's win in Gujarat and Himachal Pradesh assembly polls. The benchmark BSE Sensex today hit an all-time high of 33,956.31 by rising 119.57 points, or 0.35 per cent. Nifty scaled a new peak of 10,494.45, up 31.25 points, or 0.29 per cent.