Cyberbullying is a risk associated with the online safety of young people and, in this paper, we address one of its most common implicit forms -negation-based forms. We first describe the role of negation in public textual cyberbullying interaction and identify the cyberbullying constructions that characterise these forms. We then formulate the overall detection mechanism which captures the three necessary and sufficient elements of public textual cyberbullying -the personal marker, the dysphemistic element, and the link between them. Finally, we design rules to detect both overt and covert negation-based forms, and measure their effectiveness using a development dataset, as well as a novel test dataset, across several metrics: accuracy, precision, recall, and the F1-measure. The results indicate that the rules we designed closely resemble the performance of human annotators across all measures.