In the treatment, a reverse osmosis membrane element having a polyamide skin layer is loaded in a pressure vessel in a membrane separator and contacted with a bromide-containing aqueous solution of free chlorine. The thus treated reverse osmosis membrane element retains for a long time its effect of reducing solute concentration in a solution treated with the reverse osmosis membrane and rejects efficiently non-electrolytic organic materials or substances such as boron that will not be dissociated in a neutral region. A reverse osmosis membrane module having the thus treated reverse osmosis membrane element is provided as well.