  The isotropic majority-vote (MV) model which, apart from the one-dimensional
case, is thought to be non-equilibrium and violating the detailed balance
condition. We show that this is not true, when the model is defined on a
complete graph. In the stationary regime, the MV model on a fully connected
graph fulfills the detailed balance. We derive the exact expression for the
probability distribution of finding the system in a given spin configuration.
We show that it only depends on the absolute value of magnetization. Our
theoretical predictions are validated by numerical simulations.
