The paper considers stationary vector subdivision processes given by the bi-infinite vectors: \[ {\mathbf c}= (c_j:j\in\mathbb{Z}),\quad c_j\in \mathbb{R}^n,\;j\in\mathbb{Z}, \] a finitely supported vector: \[ {\mathbf A}=(A_j:j \in\mathbb{Z}) \text{ of }n\times n\text{ matrices}, \] and the subdivision operator: \[ S_{{ \mathbf A}^{\mathbf c}}= \sum_{k\in\mathbb{Z}} (A_{j-2k} c_k:j \in\mathbb{Z}). \] The authors provide a complete characterization of bi-infinite matrix-vectors \(A\) showing that the associated vector subdivision scheme converges in \(L_p(\mathbb{R})\) and has a limit function with a prescribed number of derivatives. These results extend and complete the author previous results on vector subdivision and their use in the construction of multiwavelets.