Let \(\mathcal {R}_{\mathcal {II}}(n)\) be the classical domain of type \(\mathcal {II}\). We first obtain a sufficient and necessary condition such that the boundary points of \(\mathcal {R}_{\mathcal {II}}(n)\) are smooth. We then establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of \(\mathcal {R}_{\mathcal {II}}(n)\).