The present invention relates to a method for preparing carboxylic acids, in particular mono- and dicarboxylic acids, by oxidative cleavage of a vicinal diol.According to the invention, said method consists of reacting a vicinal diol of formula I: where: p is an integer comprised between 1 and 6; R1 and R2 are, separately: an alkyl or hydroxyl group having 1 to 12 carbon atoms; a —(CH2)n—C02M group where n, which can be identical or different in R1 and R2, is an integer comprised between 1 and 11 and M is a hydrogen atom or an alkyl group having 1 to 4 carbon atoms or an alkaline cation; or R1 and R2 jointly form an alkylene —(CH2)m- group where m is an integer comprised between 2 and 10, preferably between 2 and 6; with industrial-grade sodium hypochlorite (or bleach), in the absence of an organic solvent and without adding a catalyst, preferably at room temperature. The invention can be used for recycling natural vegetable oils.