The metastable O2-LiCoO(2) phase undergoes several reversible phase transitions upon lithium deintercalation. The first transition leads to an unusual oxygen stacking in such layered compounds. This stacking is found to be stable for 0.52 < x < or = 0.72 in Li(x)()CoO(2) and is called T(#)2. We studied this phase from a structural viewpoint using X-ray and neutron diffraction (ab initio method). The new stacking derives from the O2 one by gliding every second CoO(2) slab by (1/3, 1/6, 0). The lithium ions are found to occupy very distorted tetrahedral sites in this structure. We also discuss the possibility of this T(#)2 phase to exhibit stacking faults, whose amount depends on the method used to prepare this deintercalated phase.