The invention concerns i) a method for treating keratinous materials, in particular human keratinous fibres such as hair, implementing a) at least one aminated and oxidised polysaccharide comprising at least one carboxy(late) group, in particular at least one aminated and oxidised inulin with one or more carboxy or carboxylate group(s); ii) a composition comprising at least the ingredient a); iii) the use of at least a) for treating keratinous fibres, in particular human keratinous fibres such as hair, and iv) a kit or device with several compartments comprising at least one ingredient a). The invention helps obtain good cosmetic conditioning properties in terms of conditioning keratinous materials, in particular hair, with a long-lasting effect.