A method of stabilizing dibenzoylmethane derivatives against UV radiation at wavelengths between 280 and 380 ran consisting essentially of adding to a sunscreen cosmetic composition consisting essentially of 1% to 3% by weight of a dibenzoylmethane derivative selected from the group consisting of 4-(1,1-dimethylethyl)-4'-methoxydibenzoylmethane and 4-isopropyldibenzoylmethane and a cosmetically acceptable medium containing at least one oily phase, an effective amount for photostabilizing said dibenzoylmethane derivative of at least 1% by weight of a substituted dialkylbenzalmalonate having formula I:
- ##STR4## wherein:
- R.sub.1 and R.sub.3 may be identical or different and represent a hydrogen atom or a C.sub.1 -C.sub.8 straight- or branched-chain alkoxy radical;
- R.sub.2 represents a C.sub.1 -C.sub.8 straight- or branched-chain alkyl radical;
- and
- R.sub.4 represents a C.sub.1 -C.sub.8 straight- or branched-chain alkyl radical,
- wherein the molar ratio of said substituted dialkylbenzalmalonate having formula (I) to said dibenzoylmethane derivative is greater than or equal to 0.6.