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Let RⅢ(n) be the classical domain of type Ⅲ with n ≥ 2.This article is devoted to a deep study of the Schwarz lemma on RⅢ (n) via not only exploring the smooth boundary points of RⅢ (n) but also proving the Schwarz lemma at the smooth boundary point for holomorphic self-mappings of RⅢ(n).