Process for the preparation of a self-invertible inverse latex comprising an aqueous phase comprising: a. a crosslinked anionic polyelectrolyte consisting, per 100 molar %, of: - a proportion between 20% and 90% of a monomer unit resulting from 2-methyl-2-[(1-oxo-2-propenyl)amino]-1-propanesulfonic acid in free acid or partially or completely salified form; - a proportion between 10% and 80% of a monomer unit resulting from at least one monomer chosen from the elements of the group consisting of acrylamide, N,N-dimethylacrylamide, methacrylamide, N-isopropylacrylamide and N-(tert-butyl)acrylamide; and - a proportion of greater than 0 molar % and less than or equal to 1 molar % of a monomer unit resulting from at least one polyethylenic crosslinking monomer chosen from methylenebis(acrylamide), ethylene glycol dimethacrylate, diethylene glycol diacrylate, ethylene glycol diacrylate, diallylurea, triallylamine, trimethylolpropane triacrylate, diallyloxyacetic acid or one of its salts, such as sodium diallyloxyacetate, or a mixture of these compounds; b. the tetrasodium salt of glutamic acid, N,N-diacetic acid, said process comprising the following stages: a) preparation of the aqueous phase as defined above, b) preparation of an organic phase comprising at least one oil and an emulsifying surfactant (S 1) system of water-in-oil type, c) mixing the aqueous phase and the organic phase prepared in stages a) and b) and emulsifying so as to form an emulsion, d) inerting the emulsion with nitrogen, e) initiating the polymerization reaction by introduction, into the inerted emulsion, of a free-radical initiator, and f) introduction, into the reaction medium resulting from stage e), of an emulsifying surfactant (S 2) system of oil-in-water type at a temperature of between 30°C and 60°C. a. a crosslinked anionic polyelectrolyte consisting, per 100 molar %, of: - a proportion between 20% and 90% of a monomer unit resulting from 2-methyl-2-[(1-oxo-2-propenyl)amino]-1-propanesulfonic acid in free acid or partially or completely salified form; - a proportion between 10% and 80% of a monomer unit resulting from at least one monomer chosen from the elements of the group consisting of acrylamide, N,N-dimethylacrylamide, methacrylamide, N-isopropylacrylamide and N-(tert-butyl)acrylamide; and - a proportion of greater than 0 molar % and less than or equal to 1 molar % of a monomer unit resulting from at least one polyethylenic crosslinking monomer chosen from methylenebis(acrylamide), ethylene glycol dimethacrylate, diethylene glycol diacrylate, ethylene glycol diacrylate, diallylurea, triallylamine, trimethylolpropane triacrylate, diallyloxyacetic acid or one of its salts, such as sodium diallyloxyacetate, or a mixture of these compounds; - a proportion between 20% and 90% of a monomer unit resulting from 2-methyl-2-[(1-oxo-2-propenyl)amino]-1-propanesulfonic acid in free acid or partially or completely salified form; - a proportion between 10% and 80% of a monomer unit resulting from at least one monomer chosen from the elements of the group consisting of acrylamide, N,N-dimethylacrylamide, methacrylamide, N-isopropylacrylamide and N-(tert-butyl)acrylamide; and - a proportion of greater than 0 molar % and less than or equal to 1 molar % of a monomer unit resulting from at least one polyethylenic crosslinking monomer chosen from methylenebis(acrylamide), ethylene glycol dimethacrylate, diethylene glycol diacrylate, ethylene glycol diacrylate, diallylurea, triallylamine, trimethylolpropane triacrylate, diallyloxyacetic acid or one of its salts, such as sodium diallyloxyacetate, or a mixture of these compounds; b. the tetrasodium salt of glutamic acid, N,N-diacetic acid, a) preparation of the aqueous phase as defined above, b) preparation of an organic phase comprising at least one oil and an emulsifying surfactant (S 1) system of water-in-oil type, c) mixing the aqueous phase and the organic phase prepared in stages a) and b) and emulsifying so as to form an emulsion, d) inerting the emulsion with nitrogen, e) initiating the polymerization reaction by introduction, into the inerted emulsion, of a free-radical initiator, and f) introduction, into the reaction medium resulting from stage e), of an emulsifying surfactant (S 2) system of oil-in-water type at a temperature of between 30°C and 60°C.