Transition metal composite hydroxide particles as a precursor to a cathode active material for use in a non-aqueous electrolyte rechargeable battery, where the transition metal composite hydroxide has secondary particles formed by an aggregation of plate-shaped primary particles and fine primary particles, are described. The secondary particles have a center section formed by the plate-shaped primary particles, a layered structure with a low-density section formed by the fine primary particles, and a high-density section formed by the plate-shaped primary particles on the outside of the center section. The average value of the ratio of the center section outer diameter to the particle size of the secondary particles is 30% to 80%, and the average value of the ratio of the high-density section radial direction thickness to the particle size of the secondary particles is 5% to 25%.