Use of at least one base in an aqueous solution, with at least one phenol substituted in position 4 of the following formula: in which R is selected from: - a benzyl group optionally substituted in the ortho and/or para and/or meta position with one or more substituents selected from a halogen, SR' and OR', R' representing a linear or branched C 1 -C 20 alkyl chain, a C 3 to C 20 cycloalkyl group, NR a R b, PR a R b, P R a R b, P OR a OR b, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl, - a linear C 1 -C 20 alkyl group, - a benzyloxy group optionally substituted in the ortho and/or para and/or meta position with one or more substituents selected from a halogen, SR' and OR', R' representing a linear or branched C 1 -C 20 alkyl chain, a C 3 to C 20 cycloalkyl group, NR a R b, PR a R b, P R a R b, P OR a OR b, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl, - a linear or branched C 1 -C 20 alkyloxy group, a linear or branched PEG-1 to 10, the -OH end group of which is alkylated with a linear or branched C 1 -C 20 alkyl, - a benzyl thioether group -S-CH 2 -Ph optionally substituted in the ortho and/or para and/or meta position with one or more substituents selected from a halogen, SR' and OR', NR a R b, PR a R b, P R a R b, P OR a OR b, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl, - a linear or branched C 1 -C 20 alkyl thioether group, of formula -S-(C 1 -C 20 -alkyl), - an -NR a R b group, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl, - a dibenzylamine group of formula -N(benzyl) 2, in which the two benzyl groups are, independently of one another, optionally substituted in the ortho and/or para and/or meta position with one or more substituents selected from a halogen, SR' and OR', R' representing a linear or branched C 1 -C 20 alkyl chain, a C 3 to C 20 cycloalkyl group, NR a R b, PR a R b, P R a R b, P OR a OR b, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl, and a source of aqueous formaldehyde, in the absence or in the presence of an organic solvent, thus constituting a reaction medium, said base being at a total concentration comprised from 0.01 to 1 equivalent, with respect to said at least one phenol substituted in position 4 of formula, said reaction medium being heated to a temperature comprised from 100 to 130°C, and said reaction medium optionally then being subjected to a heat treatment in the presence of heat transfer means, for carrying out a reaction for the preparation of a mixture of giant p - calixarenes the size of which is greater than 20. - a benzyl group optionally substituted in the ortho and/or para and/or meta position with one or more substituents selected from a halogen, SR' and OR', R' representing a linear or branched C 1 -C 20 alkyl chain, a C 3 to C 20 cycloalkyl group, NR a R b, PR a R b, P R a R b, P OR a OR b, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl, - a linear C 1 -C 20 alkyl group, - a benzyloxy group optionally substituted in the ortho and/or para and/or meta position with one or more substituents selected from a halogen, SR' and OR', R' representing a linear or branched C 1 -C 20 alkyl chain, a C 3 to C 20 cycloalkyl group, NR a R b, PR a R b, P R a R b, P OR a OR b, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl, - a linear or branched C 1 -C 20 alkyloxy group, a linear or branched PEG-1 to 10, the -OH end group of which is alkylated with a linear or branched C 1 -C 20 alkyl, - a benzyl thioether group -S-CH 2 -Ph optionally substituted in the ortho and/or para and/or meta position with one or more substituents selected from a halogen, SR' and OR', NR a R b, PR a R b, P R a R b, P OR a OR b, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl, - a linear or branched C 1 -C 20 alkyl thioether group, of formula -S-(C 1 -C 20 -alkyl), - an -NR a R b group, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl, - a dibenzylamine group of formula -N(benzyl) 2, in which the two benzyl groups are, independently of one another, optionally substituted in the ortho and/or para and/or meta position with one or more substituents selected from a halogen, SR' and OR', R' representing a linear or branched C 1 -C 20 alkyl chain, a C 3 to C 20 cycloalkyl group, NR a R b, PR a R b, P R a R b, P OR a OR b, R a and R b representing, independently of one another, a linear or branched C 1 -C 20 alkyl,