A novel significant vector (SV) regression algorithm is proposed in this paper based on an analysis of Chen's orthogonal least squares (OLS) regression algorithm. The proposed regularized SV algorithm finds the significant vectors in a successive greedy process in which, compared to the classical OLS algorithm, the orthogonalization has been removed from the algorithm. The performance of the proposed algorithm is comparable to the OLS algorithm while it saves a lot of time complexities in implementing the orthogonalization needed in the OLS algorithm.