The rupee fell back by 6 paise to end at 54.32 amid fresh dollar demand from importers ahead of the conclusion of US Fed's two-day meeting where it is widely expected to expand economic stimulus programme.At the Interbank Foreign Exchange (Forex) market, the domestic unit resumed slightly lower at 54.29 rupees from overnight close of Rs 54.26.It later moved in a narrow 19-paise range of Rs 54.15 and Rs 54.34 before concluding at Rs 54.32, showing a fall of 6 paise or 0.11 per cent.