The development of accurate methods for multilabel classification (MLC) of remote sensing (RS) images is one of the most important research topics in RS. The MLC methods based on convolutional neural networks (CNNs) have shown strong performance gains in RS. However, they usually require a high number of reliable training images annotated with multiple land-cover class labels. Collecting such data is timeconsuming and costly. To address this problem, the publicly available thematic products, which can include noisy labels, can be used to annotate RS images with zero-labeling cost. However, multi-label noise (which can be associated with wrong and missing label annotations) can distort the learning process of the MLC methods. To address this problem, we propose a novel multi-label noise robust collaborative learning (RCML) method to alleviate the negative effects of multi-label noise during the training phase of a CNN model. RCML identifies, ranks, and excludes noisy multi-labels in RS images based on three main modules: 1) the discrepancy module; 2) the group lasso module; and 3) the swap module. The discrepancy module ensures that the two networks learn diverse features, while producing the same predictions. The task of the group lasso module is to detect the potentially noisy labels assigned to multi-labeled training images, while the swap module is devoted to exchange the ranking information between two networks. Unlike the existing methods that make assumptions about noise distribution, our proposed RCML does not make any prior assumption about the type of noise in the training set. The experiments conducted on two multi-label RS image archives confirm the robustness of the proposed RCML under extreme multi-label noise rates. Our code is publicly available here.