Present invention relates to a two part coloring composition for hair with improved dyeing and conditioning properties of hair. The object of the present invention a two part hair dyeing composition consisting of Parts A and B which are mixed immediately before application onto hair wherein Part A is based on at least one hair dye and comprising further at least one amino acid surfactant and Part B is an aqueous composition and comprising at least one oxidizing agent and at least one cationic or cationizable surfactant, wherein parts A and/or B comprises additionally at least one oil.