NOVELTY - A solid electrolyte membrane is produced by forming a casting membrane by casting a dope containing a solid electrolyte and a solvent onto a support. The casting membrane is peeled from the support as a wet membrane. At least one of the casting membrane and the wet membrane is contacted with a contact liquid. The wet membrane is dried to evaporate the contact liquid from the wet membrane.    USE - The method is used for producing a solid electrolyte membrane for membrane electrode assembly and fuel cell, particularly for the proton conductive membrane in a direct methanol full cell. The solid electrolyte membrane can be used for the electrolyte in various batteries or cells such as a redox flow battery and a lithium battery, a display element, an electrochemical sensor, a signal transmission medium, a capacitor, an electrolyte membrane for electrodialysis and electrolysis, a gel actuator, salt electrolyte membrane and proton exchange membrane. The fuel cell may be used in automobiles, electric and electronic appliances for household use, mobile devices, and portable devices. Mobile devices include mobile phones, mobile notebook-size personal computers, electronic still cameras, PDA, video cameras, mobile game machines, mobile servers, wearable personal computers, and mobile displays. Portable appliances include portable generators, outdoor lighting devices, pocket lamps, electrically-powered (or assisted) bicycles. The fuel cells may also be used as power sources for robots for industrial and household use and for other toys; or as power sources for charging secondary batteries that are mounted on these appliances.    ADVANTAGE - The method produces a solid electrolyte membrane having high and uniform proton conductivity, which can be mass produced continuously by performing a membrane drying process efficiently at a short time. The fuel cell exerts excellent output density.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for:    (1) apparatus for producing the solid electrolyte membrane comprising a casting device; peeling device; a contact liquid contacting device, and a drying device;    (2) solid electrolyte membrane produced by the above method;    (3) membrane electrode assembly comprising the solid electrolyte membrane; an anode electrode being adhered to one side of the solid electrolyte membrane for generating protons from a hydrogen-containing substance supplied from outside; and a cathode electrode being adhered to the other side of the solid electrolyte membrane for synthesizing water from the protons passed through the solid electrolyte membrane and a gas supplied from the outside; and    (4) fuel cell comprising the membrane electrode assembly; and current collectors attached to the electrodes of the membrane electrode assembly for transmitting electrons between the anode electrode and outside and between the cathode electrode and the outside.    DESCRIPTION OF DRAWING(S) - The figure is an explanatory view showing a producing process of a solid electrolyte membrane.