A method for preparing a powder of an over-lithiated lamellar oxide of the following formula: Li 1+x (Mn a Ni b) 1-x O 2 wherein: * x is comprised in a range from 0.1 to 0.26; * a+b=1 with the condition that a and b are different from 0; said powder having a specific surface area ranging from 1.8 to 6 m 2 /g and having a tapped density greater than or equal to 1.6 g/cm 3, the specific surface area and the tapped density being measured as described in the description, said method comprising the following steps: a) a step for synthesizing a mixed carbonate comprising the elements Mn, Ni; b) a step for reaction of the mixed carbonate obtained in step a) with a lithium carbonate through calcination at a temperature in a range from 800 to 1,000°C, in return for which the over-lithiated lamellar oxide of the aforementioned formula is formed, the operating conditions for synthesizing the mixed carbonate being set so as to obtain a specific surface area for the lamellar oxide having a value falling under the definition of the range mentioned above, wherein the step for synthesizing a mixed carbonate consists of co-precipitating with stirring, in a basic medium, a solution comprising a manganese sulfate and a nickel sulfate and an alkaline salt carbonate, this step for synthesizing a mixed carbonate comprising the following operations: - an operation, in a reactor comprising water, for injecting a solution comprising a nickel sulfate and a manganese sulfate (a so called solution of sulfates) according to a predetermined flow rate so as to a ratio (flow rate of a solution of sulfates/volume of water) in the reactor is 0.15 mol.h -1.l -1 to 6.8 mol.h -1.l -1, a predetermined stirring rate set so as to obtain a dissipated power per unit volume ranging from 2.0 W/m 3 to 253.2 W/m 3 and at a predetermined pH ranging from 7.0 to 8.0; - an operation for maintaining the stirring of the precipitate formed for a suitable period for complete formation of the mixed carbonate; - an operation for isolating the precipitate followed by a drying operation for forming a powder of the mixed carbonate. * x is comprised in a range from 0.1 to 0.26; * a+b=1 with the condition that a and b are different from 0; said powder having a specific surface area ranging from 1.8 to 6 m 2 /g and having a tapped density greater than or equal to 1.6 g/cm 3, the specific surface area and the tapped density being measured as described in the description, said method comprising the following steps: a) a step for synthesizing a mixed carbonate comprising the elements Mn, Ni; b) a step for reaction of the mixed carbonate obtained in step a) with a lithium carbonate through calcination at a temperature in a range from 800 to 1,000°C, in return for which the over-lithiated lamellar oxide of the aforementioned formula is formed, a) a step for synthesizing a mixed carbonate comprising the elements Mn, Ni; b) a step for reaction of the mixed carbonate obtained in step a) with a lithium carbonate through calcination at a temperature in a range from 800 to 1,000°C, in return for which the over-lithiated lamellar oxide of the aforementioned formula is formed, the operating conditions for synthesizing the mixed carbonate being set so as to obtain a specific surface area for the lamellar oxide having a value falling under the definition of the range mentioned above, wherein the step for synthesizing a mixed carbonate consists of co-precipitating with stirring, in a basic medium, a solution comprising a manganese sulfate and a nickel sulfate and an alkaline salt carbonate, this step for synthesizing a mixed carbonate comprising the following operations: - an operation, in a reactor comprising water, for injecting a solution comprising a nickel sulfate and a manganese sulfate (a so called solution of sulfates) according to a predetermined flow rate so as to a ratio (flow rate of a solution of sulfates/volume of water) in the reactor is 0.15 mol.h -1.l -1 to 6.8 mol.h -1.l -1, a predetermined stirring rate set so as to obtain a dissipated power per unit volume ranging from 2.0 W/m 3 to 253.2 W/m 3 and at a predetermined pH ranging from 7.0 to 8.0; - an operation for maintaining the stirring of the precipitate formed for a suitable period for complete formation of the mixed carbonate; - an operation for isolating the precipitate followed by a drying operation for forming a powder of the mixed carbonate. - an operation, in a reactor comprising water, for injecting a solution comprising a nickel sulfate and a manganese sulfate (a so called solution of sulfates) according to a predetermined flow rate so as to a ratio (flow rate of a solution of sulfates/volume of water) in the reactor is 0.15 mol.h -1.l -1 to 6.8 mol.h -1.l -1, a predetermined stirring rate set so as to obtain a dissipated power per unit volume ranging from 2.0 W/m 3 to 253.2 W/m 3 and at a predetermined pH ranging from 7.0 to 8.0; - an operation for maintaining the stirring of the precipitate formed for a suitable period for complete formation of the mixed carbonate; - an operation for isolating the precipitate followed by a drying operation for forming a powder of the mixed carbonate.