In this paper, a novel approach for mitigating the bias within acoustic feedback cancellation in hearing aids is proposed. It is based on the use of a loudspeaker pre-whitener which considers the reduction of both its auto-correlation and its inter-correlation with the filtered microphone signal. The pre-whitener is adapted thanks to the minimization of a new criterion considering fourth order statistics of the pre-whitened input and inter-correlation between pre-whitened input and filtered output. We show, analytically and through simulations, that this technique has the potential to achieve better bias reduction than the existing approaches.