NOVELTY - A raw material containing element (A), element (M), element (X), and element (Z), is heated to obtain molten material. The obtained molten material is cooled to obtain solidified material. The obtained solidified material is crushed to obtain ground material containing solidified material and organic compound. The obtained ground material is heated under inert gas or reducing gas, to obtain positive electrode active material. The ratio of residue of organic compound, is 15 %mass or less, when heated at 700 degrees C for 8 hours under inert gas or reducing gas.    USE - Manufacture of positive electrode active material used for manufacturing positive electrode for manufacturing secondary battery (all claimed) used as power supply for electric vehicle.    ADVANTAGE - The method economically provides positive electrode active material having excellent electroconductivity, by a simple process. The secondary battery using the positive electrode active material has excellent reliability.    DETAILED DESCRIPTION - A raw material containing element (A), element (M), element (X), and element (Z), is heated to obtain molten material. The obtained molten material is cooled to obtain solidified material. The obtained solidified material is crushed to obtain ground material containing solidified material and organic compound. The obtained ground material is heated under inert gas or reducing gas, to obtain positive electrode active material which is covered with electroconductive carbon on at least one portion of the surface. The ratio of residue of organic compound, is 15 %mass or less, when heated at 700 degrees C for 8 hours under inert gas or reducing gas. The raw material composition is of formula: AaMbXcOdZe.    A=lithium, sodium or potassium;    M=iron, manganese, cobalt or nickel;    X=silicon;    Z=halo;    a,d=0.8-2.7;    b=0.6-1.4;    c=0.9-1.1;and    e=0-2.2.    INDEPENDENT CLAIMS are included for the following:    (1) manufacture of positive electrode, which involves using positive electrode active material; and    (2) manufacture of secondary battery, which involves using positive electrode.