A selective membrane having a high fouling resistance. In one embodiment, the
selective
membrane is a composite polyamide reverse osmosis membrane in which a hydrophilic
coating has been applied to the polyamide layer of the membrane, the hydrophilic
coating being made by (i) applying to the membrane a quantity of a polyfunctional
epoxy compound, the polyfunctional epoxy compound comprising at least two epoxy
groups, and (ii) then, cross-linking the polyfunctional epoxy compound in such
a manner as to yield a water-insoluble polymer.