The rupee fell by 60 paise to 63.43 against the dollar in early trade today.The rupee yesterday added 65 paise to close at one-month high of 62.83. Meanwhile, the BSE benchmark Sensex fell by 55.25 points, to trade at 19,687.22 in early trade today. Also, the wide-based National Stock Exchange index Nifty declined by 19.40 points, to 5,821.15.