NOVELTY - A spinel-type lithium manganese-containing complex oxide consists of a crystal structure belonging to Fd-3m-type spacer group. The ratio of inter-atomic distance between site (16d) and site (32e) of spinel-type lithium manganese-containing complex oxide contained in recovered supernatant with respect to inter-atomic distance between (16d) and site (32e) of the spinel-type lithium-manganese composite oxide contained in the recovered sediment is less than 101.5%, when measured by Rietveld method using a fundamental process.    USE - Spinel-type lithium manganese-containing complex oxide is used as positive electrode active material used for lithium secondary battery (all claimed) used in portable electronic devices. Uses include but are not limited to video camera, notebook computer, mobile telephone, electric vehicle, and hybrid-electric vehicle.    ADVANTAGE - The spinel-type lithium manganese-containing complex oxide effectively restrains the generation amount of gas emitted by reaction with the electrolyte solution of secondary battery.    DETAILED DESCRIPTION - A spinel-type lithium manganese-containing complex oxide consists of a crystal structure belonging to Fd-3m-type space group. The ratio of inter-atomic distance between site (16d) and site (32e) of spinel-type lithium manganese-containing complex oxide contained in recovered supernatant with respect to inter-atomic distance between (16d) and site (32e) of the spinel-type lithium-manganese composite oxide contained in the recovered sediment is less than 101.5%, when measured by Rietveld method using a fundamental process. The fundamental process is carried by introducing the spinel-type lithium manganese-containing complex oxide in an ion-exchange water at 20 degrees C, stirring for 10 minutes, allowing to stand for 2 minutes, and separating supernatant liquid and sediment. An INDEPENDENT CLAIM is included for lithium secondary battery, which contains the spinel-type lithium manganese-containing complex oxide as a positive electrode active material.