Abstract: An asymmetrical permselective cellulose triacetate membrane has outstanding properties for desalination of seawater by reverse osmosis. It is made by casting a solvent solution of the cellulose triacetate in a solvent mixture of at least 40% acetone, a solvent for the triacetate and a swelling agent for the triacetate. The swelling agent, preferably formamide, must be added as the last component of the solution. After exposing the cast solution to evaporation for 2-90 seconds, it is precipitated in cold water, and then optionally tempered at 50.degree.-100.degree. C. in water which may contain a modifying agent, and dried.