The finite resistivity of the wall that surrounds any toroidal plasma confinement device can lead to a branch of instabilities known as the resistive wall mode (RWM). Theory indicates that the RWM is potentially activated whenever the plasma equilibrium is unstable with the wall placed at infinity. In particular, advanced tokamak power plant designs require the plasma b to be above the critical value for this condition to be satisfied. Accordingly, it is important to find a method of stabilizing this mode. In this work we describe a method of stabilizing the tokamak RWM that utilizes a secondary rotating conducting shell surrounding the plasma and first wall. This scheme was first thought of for the reversed-field pinch, but must be reexamined for the tokamak as the mode involved has different characteristics. It is shown that provided the second wall is suitably positioned, RWM stabilization of a tokamak is possible even in the absence of plasma rotation.