A method of fabricating a needled fiber structure using a needling machine having a needling head with a plurality of needles, the method including placing a first fiber layer on a support; needling the first fiber layer, with the needling head being in a first position relative to the support, at least at the end of needling the first layer; after needling the first layer, implementing relative movement between the support and the needling head so as to cause the needling head to go from the first position relative to the support to a second position that is different from the first; placing a second fiber layer on the needled first fiber layer; and needling the second fiber layer placed on the first fiber layer, the needling head being in the second position relative to the support at least at the beginning of needling the second fiber layer.