Nickel manganese composite hydroxide particles and manufacturing method thereof, cathode active material for a non-aqueous electrolyte secondary battery and manufacturing method thereof, and a non-aqueous electrolyte secondary battery

To obtain a non-aqueous electrolyte secondary battery having high capacity, high output and good cyclability, nickel manganese composite hydroxide particles are a precursor for a cathode active material having lithium nickel manganese composite oxide with a hollow structure and a small and uniform particle size. An aqueous solution for nucleation includes a metallic compounds that contains nickel and a metallic compound that contains manganese, but does not include a complex ion formation agent that forms complex ions with nickel, manganese and cobalt. After nucleation is performed, an aqueous solution for particle growth is controlled so that the temperature of the solution is 60° C. or greater, and so that the pH value that is measured at a standard solution temperature of 25° C. is 9.5 to 11.5, and is less than the pH value in the nucleation step.