A method of making a fiber structure by multilayer three-dimensional weaving, the fiber structure having a thickness in a direction perpendicular to the warp and weft directions that varies along the warp direction while conserving the same number of warp yarns that are woven at all points of the fiber structure along the warp direction, wherein during a transition in the warp direction from a first portion of the fiber texture to a second portion of the fiber texture having a thickness that is greater than the thickness of the first portion, the number of warp planes is decreased and the number of layers of warp yarns is increased without changing the number of warp yarns, by constituting at least one warp plane in the second portion with warp yarns taken from at least two different warp planes in the first portion.