Method for synthesis of a material formed from particles of a carbon-coated complex oxide, wherein the complex oxide has essentially an olivine structure and the formula Li x M 1-y M' y (PO 4) n, in which: x, y and n are chosen, such that 0≤x≤2, 0≤y≤0.6 and 1≤n≤1.5; M is a transition metal or a mixture of transition metals of the first row of the periodic table; M' is an element with defined valence chosen from Mg 2+, Ca 2+, Al 3+, Zn 2+ or a combination of these elements, wherein the particles have a dimension of 0.05 to 30 μm and wherein the method is characterized in that: - the synthesis is performed by reaction in thermodynamic or kinetic equilibrium of a mixture with the required proportions of the following source compounds: a) a source for M; c) a compound source for lithium; d) a compound source for P; e) a source for conducting carbon; f) a source for M', in case y>0 with a gaseous reductive atmosphere; - the synthesis is performed while the composition of the gaseous atmosphere, the temperature of reaction and the proportion of compound source c) relative to the compound sources a), f) and d) are controlled in order to bring the oxidation state of the transition metal to a valence, which is wanted for the preparation of the compound of type LiMPO 4; - the temperature of synthesis is higher than the temperature at which the reactive atmosphere is able to reduce the one or more transition elements to the oxidation state required for the compound LiMPO 4, the temperature and the duration of synthesis are below the temperature and duration which are used to achieve reduction of the one or more transition elements to the metallic state or oxidation of carbon resulting from pyrolysis of the organic substance; - the synthesis comprises at least one pyrolysis step of compound source e). - the synthesis is performed by reaction in thermodynamic or kinetic equilibrium of a mixture with the required proportions of the following source compounds: a) a source for M; c) a compound source for lithium; d) a compound source for P; e) a source for conducting carbon; f) a source for M', in case y>0 with a gaseous reductive atmosphere; a) a source for M; c) a compound source for lithium; d) a compound source for P; e) a source for conducting carbon; f) a source for M', in case y>0 with a gaseous reductive atmosphere; - the synthesis is performed while the composition of the gaseous atmosphere, the temperature of reaction and the proportion of compound source c) relative to the compound sources a), f) and d) are controlled in order to bring the oxidation state of the transition metal to a valence, which is wanted for the preparation of the compound of type LiMPO 4; - the temperature of synthesis is higher than the temperature at which the reactive atmosphere is able to reduce the one or more transition elements to the oxidation state required for the compound LiMPO 4, the temperature and the duration of synthesis are below the temperature and duration which are used to achieve reduction of the one or more transition elements to the metallic state or oxidation of carbon resulting from pyrolysis of the organic substance; - the synthesis comprises at least one pyrolysis step of compound source e).