Preferred Definitions:    M1=a single element composition of Fe or Mn or a mixed element composition of Fe and Mn;    M2=Ti or Nb;    M3=Zr.    Provided that: when M2 is Ti, M3 is Zr.    EXAMPLE - As starting source materials, LiCH3COO as a lithium source, Fe(NO3)3.9H2O as an iron source, NbCl5 as a niobium source, H3PO4 as a phosphorus source and Si(OC2H5)4 as a silicon source were used. By setting the weight of LiCH3COO serving as the lithium source to be 1.3196 g, the above materials were weighed so that their molar ratio i.e. Li:Fe:Nb:P:Si was 1:0.95:0.05:0.85:0.15. First, the Fe source was dissolved in 30 ml of ethanol, and subsequently the Li source, Si source and Nb source were dissolved in this order. Finally, the P source which had been diluted with ethanol was mixed with the ethanol in which the other elements had been dissolved. After stirring at room temperature for one hour with a stirrer, the mixture was gelled with a drier at 60 degrees C, followed by drying to obtain a precursor. To the obtained precursor, 15 wt.% of sucrose was added, and the mixture was fired at 600 degrees C in a nitrogen atmosphere for 12 hours to synthesize a single phase powder of LiFe0.95Nb0.05P0.85Si0.15O4 which was a cathode active material of olivine type. The obtained sample was referred to as test. As starting source materials, LiCH3COO as a lithium source, Fe(NO3)3.9H2O as an iron source, ZrCl4 as a zirconium source, H3PO4 as a phosphorus source and Si(OC2H5)4 as a silicon source were used. By setting the weight of LiCH3COO serving as the lithium source to be 1.3196 g, the above materials were weighed so that their molar ratio i.e. Li:Fe:Zr:P:Si was 1:0.9:0.1:0.8:0.2. First, the Fe source was dissolved in 30 ml of ethanol, and subsequently the Li source, Si source and Zr source were dissolved in this order. Finally, the P source which had been diluted with ethanol was mixed with the ethanol in which the other elements had been dissolved. After stirring at room temperature for one hour with a stirrer, the mixture was gelled with a drier of 60 degrees C, followed by drying to obtain a precursor. To the obtained precursor, 15 wt.% of sucrose was added, and the mixture was fired at 600 degrees C in a nitrogen atmosphere for 12 hours to synthesize a single phase powder of LiFe0.9Zr0.1P0.8Si0.2O4 (M2 was not contained) which was a cathode active material of olivine type. The obtained sample was referred to as control. Cathode electrodes were formed by crushing test/control cathode active materials to form fine powder. The cathode electrodes were then used in the manufacture of non-aqueous secondary battery. The test/control material incorporating batteries were evaluated for initial discharging capacity, volume change ratio and capacity retaining ratio at 1000th time. The results for test/control material incorporating batteries were: initial discharging capacity (mAh/g) = 138.6/77.9, volume change ratio (%) = 5.0/2.9; and capacity retaining ratio at 1000th time = 83/94%. The results showed that the test cathode active material not only was excellent in view of safety and cost performance but also had a high initial discharging capacity, so that the non-aqueous secondary battery incorporating the material had a long lifetime.