This note presents a globally stable adaptive control algorithm applicable to discrete-time single-input single-output linear time- invariant systems. A priori knowledge of neither the sign of the system's high-frequency gain nor an upper-bound on its magnitude is needed to prove global stability. This last hypothesis is usually needed in other schemes. The authors first extend the approach of using Nussbaum gains to the discrete case, which then allows their use in the adaptation law. By introducing the idea of so-called switching curves, it is proved that signals can only grow with bounded increments which is a critical results in the proof of stability.