Chennai: The Indian rupee on Monday strengthened by 37 paise against US dollar during the morning trade. Opening at 66.91 to a US dollar, the Indian rupee reached a high of Rs 66.88 per US dollar. On Friday, the rupee closed at Rs 67.25. Experts are of the view that rupee would further strengthen against the US dollar intra-day in wake of poor US job data. RBI's reference rate is at Rs 66.96 per US dollar.