The composition for removing or lightening hair color is in the form of a hair color lightening suspension and is mixed with an aqueous oxidizing composition immediately prior to use. The composition includes a combination of from 0.1 to 80 percent by weight of one or more organic lipophilic compounds, namely vegetable or animal fats, vegetable or animal oils, vegetable or animal waxes, paraffin hydrocarbons, higher alcohols or ethers, aliphatic and aromatic esters and/or silicone oils; from 0.01 to 20 percent by weight of at least one lipophilic inorganic or organic thickener, which is a bentonite and/or dextrin palmitate; from 0.1 to 40 percent by weight of one or more hydrophilic inorganic or organic thickeners; from 10 to 65 percent by weight of at least one inorganic persalt; from 10 to 45 percent by weight of at least one alkaline reacting salt; and auxiliary substances and cosmetic additive ingredients, as needed.