Deep neural network (DNN) based salient object detection in images based on high-quality labels is expensive. Alternative unsupervised approaches rely on careful selection of multiple handcrafted saliency methods to generate noisy pseudo-ground-truth labels. In this work, we propose a two-stage mechanism for robust unsupervised object saliency prediction, where the first stage involves refinement of the noisy pseudo labels generated from different handcrafted methods. Each handcrafted method is substituted by a deep network that learns to generate the pseudo labels. These labels are refined incrementally in multiple iterations via our proposed self-supervision technique. In the second stage, the refined labels produced from multiple networks representing multiple saliency methods are used to train the actual saliency detection network. We show that this self-learning procedure outperforms all the existing unsupervised methods over different datasets. Results are even comparable to those of fully-supervised state-of-the-art approaches.