The two-path algorithm is an adaptive filter algorithm based on a parallel filter structure, which has been found to be useful for line echo cancellation as well as for acoustic echo cancellation. It is well known that in finite precision arithmetic, the adaptation process of adaptive algorithms can be reduced or even halted due to finite precision effects. This paper proposes a variant of the two-path scheme where the effects of quantization are reduced, without any significant increase in complexity. The improvement is shown by simulations using bandlimited flat spectrum noise as well as real speech signals.