The rupee slips to 60.4425/4450 from its previous close of 60.4335/4450.
The USD/INR pair is stuck in a narrow range as dollar gains offset by foreign buying.
Dollar index still near 13-month high.
But rupee supported as FIIs bought a net $105 million of debt on Monday and $60.4 million (provisionally) in shares on Tuesday.
The Nifty gains, nearing record highs.
(Reporting by Gaurav Pai)