A new method is developed for controlling hyperchaos in nth-order discrete systems by perturbing one of its parameters n times in a neighborhood of an unstable periodic orbit (UPO) embedded in the chaotic attractor. The method is a generalization of a recent result for controlling two-dimensional systems, and shows some advantages in comparison with classical methods for controlling chaos. Although the method is local by nature, it is shown to be robust, which allows its application in relatively large neighborhoods of the unstable orbits, and may be used in practical situations where noise, uncertainties, and external disturbances are present. To validate the applicability of the method, two different systems where stabilized, a three-dimensional hyperchaotic Hénon-like map, and a hyperchaotic generalized Hénon map, showing good performance as expected.