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Most recommender systems optimize the model on observed interaction data, which is affected by the previous exposure mechanism and exhibits many biases like popularity bias. The loss functions, such as the mostly used pointwise Binary Cross-Entropy and pairwise Bayesian Personalized Ranking, are not designed to consider the biases in observed data. As a result, the model optimized on the loss would inherit the data biases, or even worse, amplify the biases. For example, a few popular items take up more and more exposure opportunities, severely hurting the recommendation quality on niche items -- known as the notorious Mathew effect. In this work, we develop a new learning paradigm named Cross Pairwise Ranking (CPR) that achieves unbiased recommendation without knowing the exposure mechanism. Distinct from inverse propensity scoring (IPS), we change the loss term of a sample -- we innovatively sample multiple observed interactions once and form the loss as the combination of their predictions. We prove in theory that this way offsets the influence of user/item propensity on the learning, removing the influence of data biases caused by the exposure mechanism. Advantageous to IPS, our proposed CPR ensures unbiased learning for each training instance without the need of setting the propensity scores. Experimental results demonstrate the superiority of CPR over state-of-the-art debiasing solutions in both model generalization and training efficiency. The codes are available at https://github.com/Qcactus/CPR.