In Jutten's blind separation algorithm, symmetrical distribution and statistical independence of the signal sources are assumed. When they are not satisfied, the learning process becomes unstable. In order to avoid the unstable behavior, two stabilization methods are proposed. Since large samples easily disturb symmetrical distribution, the outputs of the separation process with large amplitude are detected, and the learning is skipped. Imbalance of the signal source powers affects statistical independence. It is estimated by the cross-correlation of the observed signals. When the cross-correlation is high, the correction term by the Jutten's algorithm becomes wrong. Therefore, adjusting the weights in the separation process is skipped. Computer simulation using many kinds of signal sources demonstrates the signal sources with asymmetrical distribution and imbalanced power are well separated.