The rupee fell by 37 paise to trade at nearly one-week low of 54 rupees 38 paise against the dollar in early trade today, on increased demand from oil importers and political crisis after Trinamool Congress withdrew support to the UPA government. The domestic currency had ended flat at 54 rupees 01 paise against the US currency in the previous volatile session on Tuesday. The Forex market remained closed yesterday for 'Ganesh Chaturthi'.