A t-covering array of size N, degree k, order v and strength t is an N x k array with entries from a set of v symbols such that any N x t subarray contains a t-tuple of v symbols at least once as a row. This paper presents a new algebraic recursive method for constructing covering arrays based on difference matrices. The method can extend parameter factors on the existing covering arrays and cover all the combinations of any t parameter factors （t≥2）. The method, which recursively generates high strength covering arrays, is practical. Meanwhile, the theoretical derivation and realization of the proposed algebraic recursive algorithm are given.
