The authors use a technique of L. Jorge and F. Xavier [Ann. Math., II. Ser. 112, 203-206 (1980; Zbl 0455.53004)] to construct a complete minimal surface M, which is immersed in the Euclidean space \(R^ 3\). It is of the topological type of the cylinder, transverse to the planes \(x_ 3=cons\tan t\), and such that \(| x_ 3|\) is bounded on M.