Nickel cobalt manganese composite hydroxide and process for producing same

A nickel cobalt manganese composite hydroxide with low impurity content and high reactivity when synthesizing a positive electrode active material, which can be used as a precursor of the positive electrode active material for non-aqueous electrolyte secondary batteries with low irreversible capacity, represented by a general formula: NixCoyMnzMt(OH)2+a (wherein x+y+z+t=1, 0.20≤x≤0.80, 0.10≤y≤0.50, 0.10≤z≤0.90, 0≤t≤0.10, 0≤a≤0.5, and M is at least one additive element selected from Mg, Ca, Al, Ti, V, Cr, Zr, Nb, Mo, W), which includes: spherical secondary particles formed by aggregation of a plurality of plate-shaped primary particles, which have an average particle diameter of 3 μm to 20 μm, a sulfate radical content of 1.0 mass % or less, a chlorine content of 0.5 mass % or less, and a carbonate radical content of 1.0 mass % to 2.5 mass %.