The Rupee closed stronger on Tuesday, breaking its four-day losing streak as state-run banks and foreign lenders sold dollars. The local currency opened at 90.2150 and rose to an intraday high of 90.09, supported by dollar offers from state-run banks and a change in the way the daily fixing was quoted. The rupee ended 0.1% higher at 90.1650, up from 90.2750 on Monday. The fixing reflects the premium or discount bankers are willing to pay to buy or sell dollars at the Reserve Bank of India's reference rate. This was quoted at a discount on the day, compared with a premium during most recent sessions. A discount typically signals heavier interest in selling dollars at the RBI reference rate. The rupee's recent recovery is largely a tactical bounce driven by foreign bank dollar supply and a tentative return of foreign inflows, said Dilip Parmar, forex research analyst at HDFC Securities. However, the currency remains fragile as the structural mismatch between dollar demand from importers and limited supply persists. The trend remains neutral-to-bullish for the spot rate as long as it remains above 89.90. Dollar demand from importers at any dip limited the rise in the local currency, despite dollar sales from state-run and foreign banks, traders said. Asian cues were mixed for the rupee, with the dollar index extending the pullback from Monday, while Asian currencies were rangebound. The U.S. dollar edged higher against major peers on Tuesday, with the euro weighed down by softer inflation data, but moves were fairly muted with commodity and stock markets drawing most of the day's attention. Fed funds futures are still pricing around an 80% chance that interest rates will remain on hold at the U.S. central bank's next meeting on January 27 to 28, according to the CME Group's FedWatch tool. The euro was last down 0.25% at $1.16920, giving back early small gains after data showed inflation slowed more than expected in Germany and France in December. That data sent European government bond yields down around 3 basis points, while Treasury yields were slightly higher on the day, a relative move that weighed on the common currency. Traders expect the European Central Bank to keep rates steady for all of this year, and if inflation continues to hold near its 2% target, it will have little reason to rush to hike. Against the Swiss franc , the dollar was up 0.42% to 0.795 and was up 0.15% to 156.6 on the Japanese yen . The dollar index , which measures the greenback against major currencies including the yen and the euro, rose 0.19%. Elsewhere, the Australian dollar, which is sensitive to global investor sentiment and often moves in line with stocks, has been outperforming, and hit an over one-year high of $0.6739 on Tuesday. It was last up 0.18% versus the greenback at $0.6725. Against the Chinese yuan trading offshore in Hong Kong , the U.S. dollar was flat at 6.981 yuan. The New Zealand kiwi weakened 0.14% versus the greenback to $0.578. The pound dropped in sympathy as traders thought British inflation data could follow a similar pattern, and was last down 0.30% at $1.34995, albeit after hitting a near four-month high against both the dollar and euro earlier in the day. Oil prices fell slightly on Tuesday as the market weighed expectations of ample global supply this year against uncertainty around Venezuelan crude supplies after the U.S. capture of Nicolas Maduro, the South American country's leader. Brent crude futures were down 25 cents, or 0.4%, to $61.51 a barrel by 11:54 a.m. EST (1654 GMT), while U.S. West Texas Intermediate crude fell 32 cents, or 0.6%, to $58 a barrel.......