NOVELTY - A manufacturing method of manganese composite hydroxide particles involves controlling pH of aqueous solution for nucleations which contains metallic compound containing manganese and ammonium ion supply body to 12.0-14.0 measured on basis of 25 degrees C of liquid temperature, performing nucleation, controlling pH of aqueous solution for particle growth containing nucleus to 10.5-12.0 measured on basis of 25 degrees C of liquid temperature, and making nucleus grow.    USE - A manufacturing method of manganese composite hydroxide particles used for positive electrode active material for non-aqueous electrolyte secondary batteries (claimed) used as power supply of hybrid vehicles, electric vehicles, or small portable electronic device.    ADVANTAGE - The method obtains manganese composite hydroxide particles with uniform and small particle size.    DETAILED DESCRIPTION - A manufacturing method of manganese composite hydroxide particles involves controlling pH of aqueous solution for nucleations which contains metallic compound containing manganese and ammonium ion supply body to 12.0-14.0 measured on basis of 25 degrees C of liquid temperature, performing nucleation, controlling pH of aqueous solution for particle growth containing nucleus to 10.5-12.0 measured on basis of 25 degrees C of liquid temperature, making nucleus grow, and obtaining particle which consists of manganese nickel composite hydroxide is formula Mn1-x-yNixMy(OH)2+alpha.    x=0-27;    y=0-0.05;    alpha=0-0.5; and    M=Mg, Ca, Ba, Sr, Ti, V, Cr, Zr, Nb, Mo, and/or W.    INDEPENDENT CLAIMS are included for:    (1) a manganese composite hydroxide particles;    (2) a manufacturing method of positive electrode active material for non-aqueous electrolyte secondary batteries;    (3) a positive electrode active material for non-aqueous electrolyte secondary batteries; and    (4) a non-aqueous electrolyte secondary battery.    DESCRIPTION OF DRAWING(S) - The drawing shows a flowchart of manufacturing method of manganese composite hydroxide. (Drawing includes non-English language text).