A method for fastening wrapping sheets made of paper or cellulose in pulp-bale packaging, wherein a pulp bale is wrapped using a single-piece or two-part wrapping sheet made of paper or using a lower sheet and upper sheet made of cellulose. The method is characterized in that, at the location of overlap of the two paper or cellulose sheets, or at the end fold of the wrapping sheets made of cellulose or paper, one or more clip(s), including a decomposable material, not leaving behind any harmful components, as bale processing continues, is introduced into the bale. This makes it possible to avoid a costly binding machine or paper-strapping machine, and does away with the outlay required for disposing of the wire by the end user. A fastening device which includes a decomposable material which does not leave behind any harmful components, as bale processing continues is also disclosed.