The rupee opened lower at 70.32 a dollar against 70.10 previously and dropped further to a new low of 70.65 in afternoon deals, down by 55 paise.
The local currency dropped by 49 paise or 0.70 per cent to close at 70.59 to the dollar at the interbank foreign exchange market, logging its biggest single-day drop since August 13 when it nosedived 110 paise or 1.6 per cent.
The rupee had earlier hit its all-time closing low of 70.16 on Monday.