The local currency resumed weak at 63.45 a dollar from the previous close of 63.37 at the interbank foreign exchange market and dropped to a low of 63.46.
It bounced back to a high of 63.04 on firm local equities and slipped again on dollar demand from importers, mainly oil refiners, to end at 63.38, a fall of one paisa.
On May 16, the rupee closed one paisa higher at 54.77.
The Fed's decision on tapering its monthly $85 billion bond-buying programme is expected later on Wednesday.
The outcome of the two-day Fed meeting will be known after 2 pm EST in the US (about 11:30 pm Indian time).
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