A solid polymer electrolyte comprises a matrix formed, at least partially, (a) of crosslinked polymer comprising units derived from ethylene oxide and units derived from ethylene oxide substituted with a reactive radical by substitution, at least part of which participates in a crosslinking bond, and (b) of at least an inonizable alkaline salt chelated in said matrix. In addition, a multilayer electrochemical assembly (1) comprises a positive electrode (2) and a current collector (6) of the negative electrode (3) and optionally of its current collector (5), the electrodes being separated by a solid polymer electrolyte (4), as previously described.