The invention relates to the development of an electrochemical device including a lithium salt/polyether electrolyte film between two films forming the cathode and the anode, respectively. The method of the invention involves assembling a multilayer structure consisting of the current-collecting carrier, the cathode-forming film, the electrolyte-forming polyether film and the anode-forming film. The cathode and/or anode films are made of a composite material containing the lithium salt. The polyether film is lithium salt-free. The assembled device is allowed to rest for long enough to enable the lithium salt in the cathode and/or the anode to be dispersed throughout the polymer film.