The widespread adoption of Batch Normalization (BN) in contemporary deep neural architectures has demonstrated significant efficacy, particularly in the domain of Unsupervised Domain Adaptation (UDA) for cross-domain applications. Notwithstanding its success, extant BN variants often conflate source and target domain information within identical channels, potentially compromising transferability due to inter-domain feature misalignment. To address this limitation, we introduce Refined Batch Normalization (RBN), a novel normalization paradigm that leverages estimated shift to quantify discrepancies between estimated population statistics and their expected values. Our pivotal observation reveals that estimated shift can accumulate through BN stacking within the network, potentially degrading target domain performance. We elucidate how RBN mitigates this accumulation, thereby enhancing overall system efficacy. The practical implementation of this technique is realized through the RBNBlock, which supplants conventional BN with RBN in the bottleneck architecture of residual networks. Extensive empirical evaluation across diverse cross-domain benchmarks corroborates the superiority of RBN in augmenting inter-domain transferability.