An aqueous, formaldehyde-free binder composition comprising a modified copolymer of maleic anhydride and a vinyl aromatic compound such as styrene, the copolymer being modified by reaction with a primary alkanolamine, such as monoethanolamine (MEA), to produce a modified copolymer that is self-curing and cures as a consequence of cross-linking, esterification reactions between pendant carboxyls and hydroxyl groups on the solubilized (hydrolyzed) modified copolymer chains; the invention also relates to the corresponding method of using the binder composition for making fiber products, especially fiberglass insulation.