The rupee ended flat at 105.40 against the dollar in the interbank foreign exchange market on Tuesday, dealers said. “The rupee / dollar parity traded in a narrow range of 105.41 and 105.46 in a dull activity,” a dealer said. In the open market, the rupee continued to improve, trading at 106.90 for buying and 107.20/dollar for selling as compared to the previous levels of 107 and 107.25.