Image alignment and registration methods typically rely on visual correspondences across common regions and boundaries to guide the alignment process. Without them, the problem becomes significantly more challenging. Nevertheless, in real world, image fragments may be corrupted with no common boundaries and little or no overlap. In this work, we address the problem of learning the alignment of image fragments with gaps (i.e., without common boundaries or overlapping regions). Our setting is unsupervised, having only the fragments at hand with no ground truth to guide the alignment process. This is usually the situation in the restoration of unique archaeological artifacts such as frescoes and mosaics. Hence, we suggest a self-supervised approach utilizing self-examples which we generate from the existing data and then feed into an adversarial neural network. Our idea is that available information inside fragments is often sufficiently rich to guide their alignment with good accuracy. Following this observation, our method splits the initial fragments into sub-fragments yielding a set of aligned pieces. Thus, sub-fragmentation allows exposing new alignment relations and revealing inner structures and feature statistics. In fact, the new sub-fragments construct true and false alignment relations between fragments. We feed this data to a spatial transformer GAN which learns to predict the alignment between fragments gaps. We test our technique on various synthetic datasets as well as large scale frescoes and mosaics. Results demonstrate our method's capability to learn the alignment of deteriorated image fragments in a self-supervised manner, by examining inner image statistics for both synthetic and real data.