The invention concerns the use of at least one conjugated triene-containing fatty acid for preparing a medicine for treating inflammation selected among the group consisting of alpha-eleostearic acid, catalpic acid, calendic acid, jacaric acid, licanic acid and beta-eleostearic acid for making a medicine for treating inflamatory diseases and/or metabolic disorders following an inflammation. The inflammatory diseases and/or metabolic disorders following an inflammation may be skin cancers, sun burn, benign summer light eruption, allergic and/or irritative reactions, gingivitis and periodontitis, vulvitis and vaginitis or arthritis and arthrosis. The medicine also enables healing to be promoted. Said fatty acid conjugates can also be used in the cosmetic treatment of cellulitis.