The rupee today hits new record low of 56.38 rupees in late morning trade, continuing its slide against the dollar for the seventh day in a row. In its opening session today, the rupee resumed lower at 56.20 rupees per dollar against the yesterday's closing level of 56 rupees and dropped further to an all-time low of 56.38 rupees per dollar a short while ago. Globally, the US dollar remained strong against a basket of major currencies with euro remaining under pressure as european Union leaders' pledge of united fight against the debt crisis failing to impress investors.