Rechargeable lithium cells can be made with two different intercalation compounds as the positive and negative electrodes, which are safer than the battery technology using pure Li metal. In this paper, we present our study of the Li ion type battery that uses LiTi2O4 as the negative electrode, which is coupled with a strongly oxidizing intercalation compound, spinel LiMn2O4, as the positive electrode has been found to solve problems associated with the use of metallic lithium at the expense of lowering the overall cell voltage. Preliminary electrochemical data revealed that this Li ion type battery "LiMn2O4/LiTi2O4" exhibits a low performance in terms of capacity. Li cycling efficiency is examined with mixed solvents as electrolyte. With improvements in capacity, materials such as these could improve the over all performance of secondary lithium intercalation cells.