The rupee appreciated 50 paise to 81.42 against the US dollar in early trade on Wednesday on broad dollar weakness and improving global risk sentiments.
Forex traders said sustained foreign fund inflows also supported the local unit.
At the interbank foreign exchange, the domestic unit opened at 81.43 against the dollar, then inched up to 81.42, registering a gain of 50 paise over its previous close.
On Monday, the rupee had settled at 81.92 against the US dollar.
The forex market was closed on Tuesday on account of Gurunanak Jayanti.
The rupee had strengthened on Monday and has appreciated further in offshore trading on broad US dollar weakness and positive global risk sentiment, IFA Global Research Academy said in a research note.
Flow picture is improving with FPI inflows returning into domestic equities (already close to USD 2 billion in the first few sessions of November), it added.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.01 per cent to 109.64.
Brent crude futures, the global oil benchmark, fell 0.30 per cent to USD 95.07 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 130.28 points up at 61,315.43 and the broader NSE Nifty rose 85.65 points to 18,202.80.
Foreign Institutional Investors (FIIs) were net buyers in the capital markets as they purchased shares worth Rs 1,948.51 crore on Monday, according to exchange data.