Lithium batteries have the highest energy density of all rechargeable batteries and are favoured in applications where low weight or small volume are desired-for example, laptop computers, cellular telephones and electric vehicles . One of the limitations of present commercial lithium batteries is the high cost of the LiCoO2 cathode material. Searches for a replacement material that, like LiCoO2, intercalates lithium ions reversibly have covered most of the known lithium/transition-metal oxides, but the number of possible mixtures of these [2-5] is almost limitless, making an empirical search labourious and expensive. Here we show that first-principles calculations can instead direct the search for possible cathode materials. Through such calculations we identify a large class of new candidate materials in which non-transition metals are substituted for transition metals. The replacement with non-transition metals is driven by the realization that oxygen, rather than transition-metal ions, function as the electron acceptor upon insertion of Li. For one such material, Li(Co,Al)O sub 2, we predict and verify experimentally that aluminium substitution raises the cell voltage while decreasing both the density of the material and its cost.