In this paper we determine the total edge irregularity strength of , that is a complete graph in which one of its edge has been removed. To do so, we make three cases. In two cases, the labelling of equals to the labelling of the complete graph such that no re-labelling is necessary. Meanwhile, the third case could not happen. As a result, the total edge irregularity strength of equals to the total edge irregularity strength of Kn
                        
                        
                        
                        
                            
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