The rupee fell by 37 paise to again slip below the 60 mark to 60 rupees 03 paise in early trade today, on heavy dollar demand tracking strengthening of the US currency overseas. The domestic currency had touched an all-time low of 60 rupees 76 paise against the dollar on June 26.The rupee had depreciated by 14 paise to close at 59 rupees 66 paise against the dollar yesterday.