The rupee continued its upward march and appreciated further to 41.85/87 against US currency in late morning deals following sustained portfolio inflows amid absence of intervention of the central bank.In volatile trade at the Interbank Foreign Exchange (Forex) market, the Indian unit opened steady at 41.91/93 per dollar from Monday's close of 41.90/92 a dollar.But it shot up to 41.65 on sustained dollar selling by banks to meet rupee requirements following liquidity crunch in the banking system.Later, the rupee reacted downward on some dollar buying by oil companies as well as importers and was quoted at 41.85/87 a dollar in late morning deals, still showing gains over previous close.