At the inter-bank foreign exchange market, the rupee lost 57 paise, to close at a new record low of 56.24 against the dollar.The rupee fell amid sustained month-end dollar demand from importers, and as global investors turned to the dollar as a safe haven on fresh Eurozone worries.The rupee's earlier record low was hit on May 23, when it had closed at 56 to the dollar. In the last two days, the rupee has lost 106 paise.