Blind source extraction (BSE) is a special class of blind source separation (BSS) methods, which only extracts one or a subset of the sources at a time. Based on the time delay of the desired signal, a simple but important extraction algorithm (simplified " BC algorithm")was presented by Barros and Cichocki. However, the performance of this method is not satisfying in some cases for which it only carries out the constrained minimization of the mean squared error. To overcome these drawbacks, ICA with reference (ICA-R) based approach, which considers the higher-order statistics of sources, is added as the second stage for further source extraction. Specifically, BC algorithm is exploited to roughly extract the desired signal. Then the extracted signal in the first stage, as the reference signal of ICA-R method, is further used to extract the desired sources as cleanly as possible. Simulations on synthetic data and real-world data show its validity and usefulness.