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This paper presents a new approach to the development of a family of adaptive algorithms that are robust to impulsive noise. Unlike other approaches, no cost functions or filtering of the gradient are considered in order to update the filter coefficients. Basically, the algorithm takes into account the distance between the absolute errors and the median of the absolute values of the most recent errors committed by the adaptive filter. The proposed family of algorithms can be considered as a sign-error variant of the LMS algorithm. The proposed adaptive algorithm is successfully tested in terms of accuracy and convergence in a system identification simulation in which an impulsive noise is present.