NOVELTY - A lithium-transition metal compound powder consists of secondary particles comprising primary particles with a 2 or more types of composition including lithium transition-metal type-compound having a function by which occlusion and discharge of lithium ion is possible. In a pore distribution curve, the powder has a peak in a pore radius of 80-800 nm. The primary particles of compound containing arsenic, germanium, phosphorus, lead, antimony, silicon and/or tin exist inside the secondary particles.    USE - Lithium-transition metal compound powder is used for positive-electrode materials of lithium secondary batteries (all claimed). Uses include but are not limited to notebook computers, mobile telephones, handheld video cameras, hybrid electric vehicles, electronic book players, portable printers, liquid-crystal televisions, calculators, memory cards, toys, game machine devices, timepieces, pacemakers, electric tools, and satellites.    ADVANTAGE - The lithium-transition metal compound powder enables reduction in cost, and improvement in safety, load properties, voltage properties, and bulk density, when used as a positive-electrode material in lithium secondary batteries. The powder has excellent handleability.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) manufacture of lithium-transition metal compound powder, which involves pulverizing a lithium compound, compound containing vanadium, chromium, manganese, iron, cobalt, nickel and/or copper, and a compound containing arsenic, germanium, phosphorus, lead, antimony, silicon and/or tin in a liquid medium, preparing a slurry in which the pulverized material is dispersed uniformly, spray-drying the slurry, and baking the obtained spray-dried material at 950 degrees C or more in an oxygen-containing gas atmosphere;    (2) positive electrode having an active-material layer containing the lithium-transition metal compound powder and a binder, and a collector; and    (3) lithium secondary battery provided with a negative electrode which can occlude/discharge lithium, a nonaqueous electrolyte containing a lithium salt, and the positive electrode which can occlude/discharge lithium.