A single-degree-of-freedom vibro-impact oscillator is considered. Forsome values of parameters, a non-differentiable fixed point of thePoincaré map exists: a local expansion of the Poincaré map around such apoint is given, including a square root term on the impact side. Fromthis approximate map, the stability of the fixed point can beinvestigated, and it is shown that the periodic solution is stable whenthe Floquet multipliers are real.