A multi-layer membrane which has a mixed polyamide selective layer supported on a porous polysulfone layer. The mixed polyamide selective layer includes reacted units of a polyfunctional acyl halide (e.g. trimesoyl chloride) and a diamine mixture containing 4,7,10-trioxa-1,13-tridecanediamine and a cyclic diamine (e.g. piperazine). Methods of fabricating the multi-layer membrane via techniques such as phase inversion and interfacial polymerization are described. The inventive membrane is evaluated on its water flux and salt rejection (e.g. sulfate and chloride salts) capabilities. A water desalination system containing the multi-layer membrane(s) is also provided.