A rigorous analysis of the performance of a blind source extraction structure based on a linear predictor is provided. It is shown that by minimising the mean square prediction error, it is only possible to reach a solution subject to an arbitrary orthogonal transformation, in a manner similar to the principal component analysis. To remove this uncertainty, we propose a new cost function which caters for the ambiguous power levels of the source signals. A novel adaptive blind source extraction algorithm is derived and an alternative method with prewhitening is also introduced. Simulation results verify the proposed algorithms.