Let $D$ be a Hermitian symmetric space of tube type, $G = G(D)$ its group of holomorphic diffeomorphisms, and S its Shilov boundary. To any triple $(\sigma_1, \sigma_2, \sigma_3) \in S \times S \times S$ is associated an integer $\iota (\sigma_1, \sigma_2, \sigma_3), called its Maslov index. The Maslov index is invariant under the action of $G$, is skew-symmetric with respect to the three arguments and satisfies a cocycle relation. It generalizes the classical theory of the Maslov index, where $S$ is the Lagrangian manifold and $G$ the symplectic group. The definition of the Maslov index follows previous work [Clerc, Ørsted, Transformation Groups 6 (2001) 303–320; Clerc, Ørsted, Asian J. Math. 7 (2003) 269–296], where the definition was restricted to mutually transverse triples. The key to the present extension is the use of Γ-radial convergence at a point of the Shilov boundary.