A fiber structure reinforcing a composite material part woven as a single piece by multilayer weaving between plural first and second layers of yarns. The fiber structure includes a portion of decreasing thickness that presents: plural yarn withdrawal parts in surface continuity, with yarns interrupted from the first plural layers of yarns underlying the layer of yarns of the first plural layers of yarns situated in the surface of the structure; and plural yarn withdrawal parts in surface discontinuity, with yarns interrupted from the first plural layers of yarns situated at the surface of the structure, each interrupted yarn replaced in the surface of the structure by a yarn of a layer of yarns underlying the first plural layers of yarns. The yarns of the second plural layers of yarns situated in the surface of the fiber structure are continuous over at least the entire portion of decreasing thickness.