Dealers say that the currency has been strong despite an emerging market currency rout, following worries over the Federal Reserve's QE3 tapering programme.
Also, the rupee is less vulnerable than in Sept, when it fell to a record low of 68.81 against the dollar.
The rupee is much stronger given that India has been able to control its current account deficit, much better than last year. Read more on current account deficit here
On Monday, it was likely that the RBI intervened to stem the fall in the rupee. Check currency rates here