A hollow fiber microfiltration (MF) membrane is provided. The casting solution used to make this membrane includes a fiber-forming polymer having a degree of polymerization greater than about 1000, a water-soluble polymer, an anhydride with about 2 to 12 carbon atoms, and a solvent. The membrane is formed by mixing and heating these components to form a viscous dope and then extruding the dope through an annular orifice to form a hollow fiber MF membrane. The hollow fiber membrane is then fed through a coagulation bath and two leaching baths. The membrane is especially useful for filtering liquids, such as wine and juice, so as to remove bacteria, gel, and solid particles from the liquids.