The invention relates to a cosmetic treatment method for reducing or preventing skin redness, characterized in that an effective amount of at least one compound of formula I is applied to the skin: R1-CHOH-CH(NH-COR2)(CH2OH) (I) in which R1 denotes a C13 to C17 alkoyl or alkenyl radical, R2 denotes a linear C13-C19 hydrocarbon-based radical which may comprise one or more ethylenically unsaturated groups, especially one or two ethylenically unsaturated groups, or a composition containing the compound of formula I in a physiologically acceptable medium.1 The invention also relates to the cosmetic use of the compound as a calmative.
