Method for preparing a multilayer coating for protecting against oxidation on at least one surface of at least one part made of at least one material capable of being oxidized, in which the following successive steps are carried out: a) on the surface is deposited a layer of a catalyst enabling the growth of short fibres made of a ceramic that resists oxidation; b) on the surface is grown, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, a first layer constituted of particles of a ceramic that resists oxidation, said particles comprising a majority of short fibres made of a ceramic that resists oxidation; c) the first layer is coated, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, in a totally homogeneous manner, fibre by fibre and without leaving any porosity, with a second layer made of a refractory ceramic; d) the second layer is coated, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, with a third layer made of a ceramic that resists oxidation; e) optionally, the third layer is coated, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, with a fourth layer made of a refractory ceramic; f) optionally the fourth layer is coated, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, with a fifth layer made of a ceramic that resists oxidation; g) optionally steps e) and f) are repeated 1 to 100 times, preferably 1 to 50 times; h) the part, coated on at least one of its surfaces with a refractory coating for protecting against oxidation, is recovered, said coating having a three-dimensional microstructure up to the third layer or up to the optional fifth layer; the ceramic that resists oxidation being different to the refractory ceramic. a) on the surface is deposited a layer of a catalyst enabling the growth of short fibres made of a ceramic that resists oxidation; b) on the surface is grown, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, a first layer constituted of particles of a ceramic that resists oxidation, said particles comprising a majority of short fibres made of a ceramic that resists oxidation; c) the first layer is coated, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, in a totally homogeneous manner, fibre by fibre and without leaving any porosity, with a second layer made of a refractory ceramic; d) the second layer is coated, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, with a third layer made of a ceramic that resists oxidation; e) optionally, the third layer is coated, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, with a fourth layer made of a refractory ceramic; f) optionally the fourth layer is coated, using a chemical vapour deposition CVD method or a chemical vapour infiltration CVI method, with a fifth layer made of a ceramic that resists oxidation; g) optionally steps e) and f) are repeated 1 to 100 times, preferably 1 to 50 times; h) the part, coated on at least one of its surfaces with a refractory coating for protecting against oxidation, is recovered, said coating having a three-dimensional microstructure up to the third layer or up to the optional fifth layer; the ceramic that resists oxidation being different to the refractory ceramic.