NOVELTY - A composition contains highly branched polymer (1304) having branching molecular chain containing polyalkylene-oxide chain, and primary crosslinkable group, crosslinked ethylene oxide multi-component copolymer (1306) having weight average molecular weight of 50000-300000, non-reactive polyalkylene glycol (1310) having molecular chain containing an oligoalkylene glycol chain, and lithium salt. The terminal of the molecular chain of non-reactive polyalkylene glycol is sealed by a non-reactive terminal group.    USE - Composition is used for solid electrolyte for manufacturing lithium ion secondary battery (all claimed).    ADVANTAGE - The solid electrolyte formed using the composition has excellent strength at low temperature, lithium ion conductivity, and stretching property. The lithium ion secondary battery using solid electrolyte has excellent charging/discharging characteristics.    DETAILED DESCRIPTION - A composition contains highly branched polymer having branching molecular chain containing polyalkylene-oxide chain, and primary crosslinkable group, crosslinked ethylene oxide multi-component copolymer having weight average molecular weight of 50000-300000, non-reactive polyalkylene glycol having molecular chain containing an oligoalkylene glycol chain, and lithium salt. The crosslinked ethylene oxide multi-component copolymer is a copolymer having 2 or more monomers containing ethylene oxide, and glycidyl ether having secondary crosslinkable group capable of reacting with primary crosslinkable group. The terminal of the molecular chain of non-reactive polyalkylene glycol is sealed by a non-reactive terminal group. INDEPENDENT CLAIMS are included for the following:    (1) solid electrolyte, which has matrix (1302) having nanostructure in which non-reactive polyalkylene glycol is held onto a co-crosslinked component (1308) formed by chemically crosslinking the highly branched polymer and crosslinkable ethylene oxide multicomponent copolymer, and lithium salt which is dissolved in the matrix;    (2) lithium ion secondary battery, which has a negative electrode active material layer, positive electrode active material layer, and solid electrolyte layer interposed between the negative electrode active material layer and positive electrode active material layer. The negative electrode active material layer contains lithium ion conductive solid electrolyte (a), negative electrode active material and primary conductive support agent which are dispersed to the solid electrolyte (a). The positive electrode active material layer contains lithium ion conductive solid electrolyte (b), positive electrode active material and secondary conductive support agent which are dispersed to solid electrolyte (b). The solid electrolyte layer contains lithium ion conductive solid electrolyte (c); and    (3) manufacture of lithium ion secondary battery. Layer (A) is formed by dispersing negative electrode active material and primary conductive support agent to primary precursor mixture, and irradiating. Layer (B) is formed by dispersing positive electrode active material and secondary conductive support agent to secondary precursor mixture, and irradiating. The layer (C) containing precursor mixture, is formed by electron beam irradiation. A tension alignment component is formed by interposing layer (C) between layer (A) and layer (B), and electron beam is irradiated to the obtained tension alignment component to obtain lithium ion secondary battery.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of matrix of solid electrolyte.    Matrix (1302)    Highly branched polymer (1304)    Crosslinked ethylene oxide multi-component copolymer (1306)    Co-crosslinked component (1308)    Non-reactive polyalkylene glycol (1310)    Crosslinked points (1312,1313,1314)