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Unsupervised domain adaptation studies how to transfer a learner from a labeled source domain to an unlabeled target domain with different distributions. Existing methods mainly focus on matching the marginal distributions of the source and target domains, which probably lead a misalignment of samples from the same class but different domains. In this paper, we deal with this misalignment by achieving the class-conditioned transferring from a new perspective. We aim to maximize the conditional independence of feature and domain given class in the reproducing kernel Hilbert space. The optimization of the conditional independence measure can be viewed as minimizing a surrogate of a certain mutual information between feature and domain. An interpretable empirical estimation of the conditional dependence is deduced and connected with the unconditional case. Besides, we provide an upper bound on the target error by taking the class-conditional distribution into account, which provides a new theoretical insight for most class-conditioned transferring methods. In addition to unsupervised domain adaptation, we extend our method to the multi-source scenario in a natural and elegant way. Extensive experiments on four benchmarks validate the effectiveness of the proposed models in both unsupervised domain adaptation and multiple source domain adaptation.