MUMBAI: The rupee continued its rally against the dollar and strengthened by about two paise to 42.43/44 at a fairly active interbank forex market today. Opening at 42.45/46, the rupee eased slightly to 42.46/47 in the morning on some corporate covering and lower supply. It moved upto 42.42/43 level in the afternoon before closing at 42.43/44 as against 42.45/46 of the previous day.