PURPOSE: To give an excellent wet color fastness without reducing other color fastness by treating a dyed material composed of a cellulose-based fiber dyed with a direct dye or a reactive dye with a specified polymer.

CONSTITUTION: A cellulose-based fiber material dyed with a direct dye or a reactive dye is treated in a bath composed of an alkaline liquid containing (A) a polymer composed of a repeating monomer unit represented by the formula (X is a halogen; Y is an organic acid or an inorganic acid) and (B) a polymer composed of the repeating monomer unit represented in the above-mentioned (A) and another repeating monomer units such as anallylic and an acrylic repeating monomer units (a preferable example; diallyldimethyl-ammonium chloride) derived from a monomer copolymerizable with a monomer deriving the above-mentioned repeating monomer unit so as to improve the wet color fastness. In addition, the polymer represented by (A) is obtained by polymerizing a salt a reaction product between diallylamine and an epihalohydrin.