TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The core comprises a lithium nickel composite oxide component such as (Lia(NixM1yM2z)O2), (Lia(NixCoyMnz)O2), where M1 is cobalt, manganese, nickel, aluminum, magnesium and titanium, M2 is calcium, magnesium, aluminum, titanium, strontium, iron, cobalt, manganese, nickel, copper, zinc, yttrium, zirconium, niobium and boron, a is less than or equal to 1.2, but more than 0.8,, x is 0.6-1, y is 0-0.4, z is 0-0.4 and x+y+z is less than or equal to 1.2. The coating layer further comprises an alkali metal, an alkaline earth metal, a transition metal, and a Group 15 element, lithium, sodium, potassium, rubidium, cesium, magnesium, calcium, aluminum, silicon, tin, lead, manganese, iron, chromium, nickel, zinc, zirconium, thallium and nitrogen. The sulfate compound comprises an alkali metal, an alkaline earth metal, a transition metal, and a Group 15 element. Preferred Composition: The lithium nickel composite oxide component comprises 60 mole% or more nickel based on total number of moles of metal atoms except lithium in the component. The concentration of the sulfur component is 0.01-10 wt.% based on a total weight of the positive active material. The concentration of the sulfate compound is 0.01-10 pts. wt. based on 100 pts. wt. core.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The sulfate compound further comprises compound of formula (I), preferably sodium dodecyl sulfate, lithium dodecyl sulfate, ammonium lauryl sulfate and sodium lauryl sulfate.R = aliphatic hydrocarbon (optionally substituted), preferably 1-20C alkyl;X = alkali metal, alkaline earth metal, Group 13 element, Group 14 element, transition metal, rare earth element or ammonium ion, preferably NH4, Li, Na, K, Rb, Cs, Mg, Ca, Al, Si, Sr, Pb, Mn, Fe, Cr, Ni, Zn, Zr and Tl; anda, b = 1-5.Preferred Process: The method further involves washing the core with distilled water before coating the surface of the core with the coating solution. The heat-treating step is performed by carrying out drying and calcination at 300-1000 degrees C in air.