NOVELTY - A positive electrode active material contains a lithium complex oxide having an olivine-type structure. Portion(s) of the surface of lithium complex oxide is coated by a carbon material. The area ratio (SD/SG) between carbon D band and carbon G band found using Raman measurement is 3.5 or more. The complex oxide has specific surface area (S) of 13 m2/g2/g. The ratio (d/D) between particle diameter (d) and the crystallite diameter (D) found from the half width obtained using X-ray diffraction is 1-1.35.    USE - Positive electrode active material for positive electrode of non-aqueous secondary battery (all claimed) used as power supply for motor vehicles.    ADVANTAGE - The positive electrode active material is baked at low temperature to achieve small particle diameter, and has reduced manganese elution during high temperature storage.    DETAILED DESCRIPTION - A positive electrode active material contains a lithium complex oxide having an olivine-type structure of formula: LiaMnxM1-x(PO4)b.    a,b=0.8-1.2;    x=0.3 or more and less than 1;and    M=Li, Fe, Ni, Co, Ti, Cu, Zn, Mg or Zr.    Portion(s) of the surface of lithium complex oxide is coated by a carbon material. The area ratio (SD/SG) between carbon D band and carbon G band found using Raman measurement is 3.5 or more. The complex oxide has specific surface area (S) of 13 m2/g2/g. The ratio (d/D) between particle diameter (d) and the crystallite diameter (D) found from the half width obtained using X-ray diffraction is 1-1.35. INDEPENDENT CLAIMS are included for the following:    (1) manufacture of positive electrode active material, which involves mixing the raw material of lithium complex oxide, carrying out temporary baking, mixing a carbon source with the calcination product, and carrying out actual baking. The calcination temperature in the process of actual baking is more than the crystallization temperature of lithium complex oxide, and less than 400 degrees C; and    (2) non-aqueous electrolyte secondary battery having the positive electrode active material.