Abstract: A porous electrolyte membrane including a first main surface and a second main surface that are separated by a thickness, where carbon nanotubes, defining through-pores or through-channels that are open at their two ends, have a diameter smaller than or equal to 100 nm, are oriented in the direction of the thickness of the membrane, and are all substantially parallel over the entire thickness of the membrane, connect the first main surface and the second main surface; the carbon nanotubes are separated by a space, and the space between the carbon nanotubes is completely filled with at least one solid material, and an electrolyte is confined inside the carbon nanotubes. A method for preparing the membrane and an electrochemical device, such as a lithium accumulator or battery, including the electrolyte membrane.