Abstract: A fused solid-state electrolyte e membrane having a thickness less than 5 mm and intended for a lithium-ion battery. The membrane includes a polycrystalline product including at least 3.0% amorphous phase and including, for more than 95% of its mass, of the elements Li, La, Zr, M and O, M being a dopant chosen from the group formed by Al, P, Sb, Sc, Ti, V, Y, Nb, Hf, Ta, the lanthanides with the exception of La, Se, W, Bi, Si, Ge, Ga, Sn, Cr, Fe, Zn, Na, K, Rb, Cs, Fr, Mg, Ca, Sr, Ba and the mixtures thereof. The contents of these elements, measured after a decarbonatation operation without loss of lithium, being defined by the formula LiaLabZrcMdO12, wherein the atomic indices are such that: 2.500<a<8,500, and 1,000<b<3.500, and 0.600<c<2.000, and 0<d<2.000.