It is well known that exponentially unstable linear systems can not be globally stabilized in the presence of input constraints. In the case where the linear system is neutrally stable, one can achieve global asymptotic stability using a particular control Lyapunov function (CLF)-based controller. Using this particular CLF as terminal cost in a receding horizon scheme, we obtain a receding horizon controller which globally stabilizes such systems. Contrary to previous results, the horizon length is fixed, and can be chosen arbitrarily. The resulting controller also outperforms the CLF controller, since it provides a lower cost as measured by a quadratic performance index.