The k-ary n-cube is one of the most popular interconnection networks for parallel computing. This paper addresses the size of a largest connected component of a faulty k-ary n-cube. We prove that, in a k-ary n-cube (k >= 4 and n >= 2) with up to 4n–2 faulty vertices, all fault-free vertices but at most two constitute a connected component. Moreover, this assertion holds if and only if the set of all faulty vertices is equal to the neighborhood of a pair of fault-free adjacent vertices.