A lithium or lithium-ion rechargeable battery with improved cycling performance, comprising an anode made of lithium optionally alloyed with other metals, or an anode of an electrically conductive material wherein lithium is intercalated in ionic form, a non-aqueous electrolyte and a cathode based on a manganese spinel modified by the substitution of a portion of manganese with an equal amount of gallium, according to the following formula:
- LiGaxMn2−xO4
- wherein:
- 0<x≦0.1
- characterized in that said rechargeable battery has a nominal voltage of 4 V, and in that said modified manganese spinel is obtained by mixing together LIOH, MnO2 and a gallium compound, and heating the mixture to a temperature from 650° C. to 850° C.