The present invention relates to a positive electrode active material, a negative electrode active material and an electrolyte that are used alone or in combination to improve charge and discharge cycle characteristic, low temperature characteristic and safety of a non-aqueous electrolyic secondary battery, particularly a lithium ion secondary battery. Specifically, a particulate Li-transition metal composite oxide having an average particle size of not less than 10 µm, wherein [20/(specific surface area×average particle size)]=7- 9 , is used as a positive electrode active material.