A method for preventing a redeposition during washing of dyed fabric or garments made from natural and synthetic fibers is provided. The method may include admixing 0.1% to 1% of at least one anti-redeposition agent to an aqueous bath depending on the total weight of the dyed fabric to be washed. The anti-redeposition agent may include a water-soluble polyester made from bio-renewable raw materials. The water-soluble polyester may include a reaction product of a polyglycerol mixture, a sugar alcohol, a sebacic acid, and one of an unsaturated fatty acid, a saturated fatty acid, a fat or an oil, a polylactic acid, or polyhydroxyalkanoate.