The famous FastICA algorithm has been widely used for blind signal separation. For every process, it only converges to an original source which has the maximum negentropy of the underlying signals. To ensure the first output is the desired signal, we incorporate a priori knowledge as a constraint into the FastICA algorithm to construct a robust blind source extraction algorithm. One can extract the desired signal if its normalized kurtosis is known to lie in a specific range, whereas other unwanted signals do not belong to this range. Experimental results on biomedical signals illustrate the validity and reliability of the proposed method.