The present invention relates to a use of a cosmetic composition for removing make-up, in particular waterproof make-up, wherein the cosmetic composition is in the form of a water-in-oil emulsion. The cosmetic composition, which is coated onto or impregnated into an applicator for cosmetic purpose, such as a pad, comprises an oil component having a polarity of at least 20 mN/m, water, and an emulsifier component comprising a lipophilic non-ionic emulsifier. According to another aspect, the invention relates to a method for removing make-up, especially waterproof make-up, comprising applying the above cosmetic composition to the skin. Further, the present invention is concerned with a specific cosmetic composition comprising water, an emulsifier component comprising a lipophilic non-ionic emulsifier, and an oil component which is a mixture of C 12 -C 16 alkane and a cyclic silicone, in particular a cyclopentasiloxane and/or cyclohexasiloxane, and also to an applicator for cosmetic purpose impregnated or coated with such cosmetic composition. The present invention allows a highly efficient removal of waterproof make-up while reducing or avoiding the formation of an oily or greasy film with heavy texture on the skin upon use.