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The n-dimensional hypercube is one of the most popular topological structure for interconnection networks in parallel computing and communication systems. The exchanged hypercube EHðs; tÞ, a variant of the hypercube, retains several valuable and desirable properties of the hypercube such as a small diameter, bipancyclicity, and super connectivity. In this paper, we construct s þ 1 (or t þ 1) internally vertex-disjoint paths between any two vertices for parallel routes in the exchanged hypercube EHðs; tÞ for 3 s t. We also show that both the ðs þ 1Þ-wide diameter and s-fault diameter of the exchanged hypercube EHðs; tÞ are s þ t þ 3 for 3 s t.