In this paper, a new computationally efficient algorithm for recursive least-squares (RLS) filtering is presented. The proposed Split RLS algorithm can perform the approximated RLS with O(N) complexity for signals having no special data structure to be exploited, while avoiding the high computational complexity (O(N2)) required in the conventional RLS algorithms. Our performance analysis shows that the estimation bias will be small when the input data are less correlated. We also show that for highly correlated data, the orthogonal preprocessing scheme can be used to improve the performance of the Split RLS. Furthermore, the systolic implementation of our algorithm based on the QR- decomposition RLS (QRD-RLS) arrays as well as its application to multidimensional adaptive filtering is also discussed. The hardware complexity for the resulting array is only O(N) and the system latency can be reduced to O(log2 N). The simulation results show that the Split RLS outperforms the conventional RLS in the application of image restoration. A major advantage of the Split RLS is its superior tracking capability over the conventional RLS under non-stationary environments.