A reduced odor composition is composed of at least one cationic polygalactomannan or a derivative of cationic polygalactomannan having a weight average molecular weight (Mw) having a lower limit of 5,000 and an upper limit of 200,000, a light transmittance in a 10% aqueous solution of greater than 80% at a light wavelength of 600 nm, a protein content of less than 1.0% by weight of polysaccharide, and a trimethylamine content of less than 25 ppm in a 10% aqueous solution of the polymer. This composition is prepared by treating the polymer with reagents that reduce the molecular weight of the polymer, removing the water-insoluble solid material, and removing odorous components, including trimethylamine (TMA) and other amines and low molecular weight components from the aqueous phase to produce a polymer that when used in a functional system such as household care, personal care or pet care products has reduced or no odor at acidic, neutral, or alkaline pH values.