A composite member having increased resistance to delamination includes a reinforcing wrap of fiber-matrix composite material which is encircled about the member so that the edge surfaces of the member are covered by the wrap. The wrap includes fibers which are oriented from about -60.degree. to about +60.degree. relative to the direction along which the reinforcing wrap is wrapped about the member. The fibers of the reinforcing wrap impart increased third-axis or Z-direction strength at the edges of the member where interlaminar tensile stresses are greatest.