NOVELTY - The installation comprises two electrochemical reactors (R1, R2) including sets of elementary electrochemical cells, an element connector comprising an anodic compartment that circulates gas to cathodes and a cathodic compartment that circulates gas to the anodes, and heat exchangers (13.1, 13.2) where one of the heat exchangers is fluidly connected in series to an exit of one of the compartments of one of the reactors and an entry of one of the compartments of the other of the reactors while the other heat exchanger is fluidly connected to an external heat source (14) with the reactors.    USE - The installation for electrolyzing water vapor at high temperature or producing electricity in a solid oxide fuel cell (claimed) is useful for producing allothermal hydrogen.    ADVANTAGE - The installation strongly functions in an allothermic mode with a high steam conversion rate, optimizes electricity consumption, and avoids the integration of the heat exchangers within the stacking of the cells thus reducing investment costs and maintenance.    DETAILED DESCRIPTION - The installation comprises two electrochemical reactors (R1, R2) including sets of elementary electrochemical cells, where the cells comprise cathodes, anodes and electrolytes inserted between the cathodes and the anodes, an element connector comprising an anodic compartment that circulates gas to the cathodes and is arranged in electrical contact with the cathodes and a cathodic compartment that circulates gas to the anodes and is arranged in electrical contact with the anodes, where the electrochemical reactors are connected fluidly in series with each other by the compartments of gas circulation, and heat exchangers (13.1, 13.2) where one of the heat exchangers is fluidly connected in series to an exit of one of the compartments of gas circulation of one of the reactors and an entry of one of the compartments of gas circulation of the other of the reactors while the other heat exchanger is fluidly connected to an external heat source (14) with the reactors. Each reactor includes the element connector arranged between two adjacent basic cells and has an electrical contact with an electrode of one of the two basic cells and an electrode of the other of the two basic cells. An exit of the other of the compartments is connected to an independent circuit. The reactors are fluidly connected in parallel with each other in its downstream part. An INDEPENDENT CLAIM is included for a method for electrolyzing water vapor at high temperature.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of an operation of an installation of electrolysis to water vapor at high temperature.    Heat exchangers (13.1, 13.2)    External heat source (14)    Electrochemical reactors. (R1, R2)