The invention relates to the use, as agent for depigmenting and/or whitening the skin, in particular for eliminating pigmentary spots and/or senescence spots, and/or as anti-browning agents, of a compound of formula (I): R1—CHOH—CH(NH—COR2)(CH2OH)  (I) in which R1 denotes a C11 to C21 alkyl radical, and R2 denotes a linear, optionally hydroxylated C11-C19 hydrocarbon-based radical, with the hydroxyl group being in the alpha-position with respect to the carbonyl, which may comprise one or more ethylenic unsaturations, in particular one or two ethylenic unsaturations. The invention also relates to a cosmetic process for depigmenting and/or lightening skin exhibiting pigmentation spots, comprising the application to the skin of a composition comprising, in a physiologically acceptable medium, a compound of formula (I).