1. A positive electrode active material for a lithium ion battery, comprising a lithium
transition metal-based oxide powder, the powder comprising single crystal monolithic
particles comprising Ni and Co and having a general formula Lii+a ((Niz(Nii/2Mni/2)yCox)i-i<
Ak)i-a 02, wherein A is a dopant, -0.020.90,
- sintering the second mixture in an oxidizing atmosphere at a temperature between (950-(155.56*z))°C and (1050-(155.56*z))°C, for a time between 6 and 36 hrs,
- milling the sintered second mixture whereby the sintered second mixture particles are separated in solitary primary particles,
- providing a Co-based precursor and mixing said precursors with the sintered and milled second mixture, thereby obtaining a third mixture having a Li to transition metal ratio in the third mixture LM3 with -0.107*z+1.0180, z>0.35 and -0.012LM1 and LM3>LM1, and the second sintering temperature is between 895°C and 995°C.
11. The method according to anyone of claims 8 to 10, wherein LM3 = LM2.
12. The method according to claim 10 or 11, wherein between 2 and 10 mol% of Co is added in the Co-based precursor, whereby the mol% Co is expressed versus the total metal content except Li in the second mixture.

13. The method according to anyone of claims 8 to 12, wherein the milling step is applied t break agglomerated powder obtained after sintering the second mixture into separate particles in a ball mill equipment.
14. The method according to anyone of claims 8 to 13, wherein the method comprises the subsequent steps of:

- providing an inorganic oxidizing chemical compound,
- providing a chemical that is a Li-acceptor,
- mixing the sintered third mixture, the oxidizing compound and the Li-acceptor, thereby obtaining a fourth mixture, and
- heating the fourth mixture at a temperature between 300 and 800°C in an oxygen comprising atmosphere.

15. The method according to claim 14, wherein both the inorganic oxidizing chemical compound and the Li-acceptor chemical are the same compound, being either one of U2S2O8, H2S2O8 and Na2S20s, and the heating temperature of the fourth mixture is betweer 350 and 450°C.
16. The method according to claim 14 or 15, wherein a nanosized AI2O3 powder is provided as a further Li-acceptor chemical.
17. Use of the powderous positive electrode material of anyone of claims 1 to 7 in either a solid state lithium ion battery, or in a lithium ion battery provided with a liquid electrolyte, and being cycled up to a voltage or at least 4.35V.