NOVELTY - A solution (S) of a water-soluble iron precursor, a water-soluble manganese precursor, phosphoric acid and optionally a water-soluble dopant metal precursor in water and/or alcoholic co-solvent is formed. A solution of lithium hydroxide in water or mixture of water and alcoholic co-solvent is added to the solution (S) at 80 degrees C or more. The resulting solution is heated to 100 degrees C or more and up to the boiling temperature of the solution to form the olivine lithium manganese iron phosphate.    USE - Co-precipitation method for preparing olivine lithium iron manganese phosphate particles for cathode of lithium battery (all claimed) used as power supply for vehicles and electronic equipments.    ADVANTAGE - The olivine lithium iron manganese phosphate particles having high electroconductivity are produced, and provide lithium battery having high energy density and power density and excellent cycle characteristics.    DETAILED DESCRIPTION - A solution (S) of a water-soluble iron precursor, a water-soluble manganese precursor, phosphoric acid and optionally a water-soluble dopant metal precursor in water and/or alcoholic co-solvent is formed. The molar ratio of iron to manganese is 0.1:0.9-0.9:0.1. The content of dopant metal is 3 mol% or less based on the total moles of iron, manganese and dopant metal. The molar ratio of iron, manganese and dopant metal combined to phosphoric acid is 0.75:1-1.25:1. A solution of lithium hydroxide in water or mixture of water and alcoholic co-solvent is added to the solution (S) at 80 degrees C or more. The molar ratio of lithium to phosphate ions is 2.5-3.5:1. The mixture contains 0.1-0.8 moles phosphate ions per liter of water/co-solvent mixture, after addition of lithium hydroxide solution. The weight ratio of water and co-solvent after the addition of the lithium hydroxide solution is 20:80-75:25. The weight ratio of water and co-solvent after addition of the lithium hydroxide solution is 20:80-60:40 when the mixture contains 0.2 moles or less phosphate ions per liter of water/co-solvent mixture. The resulting solution is heated to 100 degrees C or more and up to the boiling temperature of the solution to form the olivine lithium manganese iron phosphate. An INDEPENDENT CLAIM is included for lithium battery.