The rupee strengthened further by 20 paise to 65.81 against the dollar in early trade today, largely supported by recent RBI measures. The domestic currency had gained 106 paise to close at 66.01 yesterday against the dollar after steps taken by new RBI Governor Raghnuram Rajan to attract US currency inflows. Dealers said, besides increased dollar selling by exporters, a higher opening in domestic equity market and dollar's weakening against some currencies overseas helped the rupee rise.