For the first time ever, the Indian Rupee has hit a historical low of 80 against the US dollar on Tuesday.

The fall could be even steeper, as a break of key psychological rate increases bets in favour of a free fall after, as the rupee weakened beyond the 77 per dollar rate.

This is the seventh straight session of record lows for rupee.

Today morning, the Sensex was at 54,389.79 points, down 131.36 points or 0.24 per cent, whereas Nifty was at 16,252.95 points, down 25.55 points or 0.16 per cent.

According to the National Stock Exchange data, 29 were in the green and the rest in the red among the Nifty 50 stocks.

Consistent depreciation in the value of the rupee has been weighing on the domestic stocks. A depreciation in the rupee is typically negative for foreign investors.

"We expect a rupee to remain volatile this week and could hold its key support level of 80.5500 on a closing basis," brokerage Prithvi Finmart told ANI.

It may be mentioned that the rupee has been battered by an exodus of foreign investors, widening trade and current account deficits and driven by a global stampede into safe-haven US dollars on rising global recession risks.

This year, foreign fund outflows from the country are more than the combined inflows of the last two years, with foreign investors pulling out a record $29 billion from Indian assets.