We consider one class of bursting oscillation models, that is square-wave burster. One of the interesting features of these models is that periodic bursting solution need not to be unique or stable for arbitrarily small values of a singular perturbation parameter $epsilon$. Recent results show that the bursting solution is uniquely determined and stable for most of the ranges of the small parameter $epsilon$. In this paper, we present a condition of uniqueness and stability of periodic bursting solutions for all sufficiently small values of $epsilon$ > 0.