In this study, we investigated a phenomenon that one intuitively would assume does not exist: self-citations on the paper basis. Actually, papers citing themselves do exist in the Web of Science (WoS) database. In total, we obtained 44,857 papers that have self-citation relations in the WoS raw dataset. In part, they are database artefacts but in part they are due to papers citing themselves in the conclusion or appendix. We also found cases where paper self-citations occur due to publisher-made highlights promoting and citing the paper. We analyzed the self-citing papers according to selected metadata. We observed accumulations of the number of self-citing papers across publication years. We found a skewed distribution across countries, journals, authors, fields, and document types. Finally, we discuss the implications of paper self-citations for bibliometric indicators.