A rigorous analysis of the blind source extraction (BSE) approach based on a linear predictor is provided. It is shown that by minimising the mean squared prediction error (MSPE), as originally proposed, it is only possible to reach a solution subject to an arbitrary orthogonal transformation. To remove this ambiguity, a new cost function based on the normalised MSPE is introduced which by design provides a unique solution to this class of BSE problems. Depending on whether the pre-whitening operation is required or not, a novel class of BSE algorithms are derived and approaches with both fixed and adaptive linear predictor coefficients are considered. The proposed algorithms are justified by both the analysis and simulation results.