thus positive electrode active materials in each of which had a boron oxide layer formed on the surface thereof were obtained using the obtained positive electrode active materials positive electrodes were prepared and using the resultant positive electrodes test cells were prepared the prepared test cells were evaluated in the same manner as described in the foregoing the results of the evaluation are shown in table 3 table 3 also shows the results for comparative example 1 as shown in table 3 even when b 2 o 3 was used as the coating treatment agent the test cells according to the invention exhibited higher discharge capacities at the first cycle than comparative example 1 in which the boron oxide layer was not formed a lithium containing transition metal oxide having the composition li 1 04 mn 0 32 co 0 32 ni 0 32 o 2 was prepared in the same manner as described in experiment 1 above except that a coprecipitated hydroxide with a varied composition ratio of mn co and ni was prepared as in the preparation of the lithium containing transition metal oxide in experiment 1 and the resultant coprecipitated hydroxide and lithium hydroxide were mixed at a predetermined composition ratio using h 3 bo 3 as the coating treatment agent the lithium containing transition metal oxide was mixed with aqueous solutions containing h 3 bo 3 in amounts of 1 part by mass for example 11 and 2 parts by mass for example 12 with respect to 100 parts by mass of the lithium containing transition metal oxide the mixtures were dried at 80 u00b0 c and thereafter heat treated in the air at 300 u00b0 c for 5 hours thus positive electrode active.