Nickel manganese composite hydroxide particles that are expressed by a general formula NixMnyCozMt(OH)2+a wherein x+y+z+t=1, 0.3≦x≦0.7, 0.1≦y≦0.55, 0≦z≦0.4, 0≦t≦0.1, 0≦a≦0.5, and M is one or more added element that is selected from among Mg, Ca, Al, Ti, V, Cr, Zr, Nb, Mo and W, and that are spherical shaped secondary particles that are formed by a plurality of aggregate primary particles, wherein the secondary particles have an average particle size of 3 to 7 μm, a value of (d90−d10)/average particle size, which is an index indicating the extent of the particle size distribution, of 0.55 or less, the particles having a center section comprising fine primary particles, and an outer shell section on the outside of the center section comprising plate shaped or needle shaped primary particles that are larger than the fine primary particles, with the thickness of the outer shell section being 0.3 to 3 μm.