In the framework of this work, the compositions Li (Ni0.33Mn0.33Co0.33)1-xFexO2 (0 ≤ x ≤ 1) of the tetrahedron LiNiO2-LiMnO2-LiCoO2-LiFeO2 were investigated. The samples were synthesized by the gel combustion method with starch. For the first time it was obtained without admixtures LiNi0.2Mn0.2Co0.2Fe0.4O2 solid solution with a layered crystalline structure a-NaFeO2, which can be used as a cathode material of lithium-ion batteries. An electrochemical testing of the homogeneous sample LiNi0.2Mn0.2Co0.2Fe0.4O2 and the sample with a minimum iron content LiNi0.3Mn0.3Co0.3Fe0.1O2 was conducted. The results show feasibility of further studying the homogeneity region and the properties of the solid solution Li (Ni, Mn, Co, Fe)O2.