The well known Least Mean Square (LMS) algorithm, or variations thereof are frequently used in adaptive systems. When the LMS algorithm is implemented in a finite precision environment it suffers from quantization effects. These effects can severely degrade the performance of the algorithm. This paper proposes a modification of the LMS algorithm that reduces the impact of quantization at virtually no extra computational cost. The paper contains an off-line evaluation of a system identification scheme where the presented algorithm outperforms the classical LMS algorithm yielding a better modelling of the unknown plant. This approach is well suited for adaptive system identification, e.g. beam-forming, electrocardiography, and echo cancelling.