Seminal studies on negation revealed that negative sentences are difficult to process, as they require an extra mental step. Similarly, at the discourse level, concession has been repeatedly shown to be more complex than other relations such as result because it implies the denial of an inference. The affinity between negation and concession prompted the present study to test whether overt verb polarity would affect the processing of upcoming discourse relations. In particular, it investigated whether negation can act as a cue to help process concessive relations. Results from four self-paced reading experiments indeed show a robust facilitation effect of negation on concession that cancels the baseline difference between concessive and result relations, thus nuancing existing context-blind categorizations of concession as a highly complex relation. This study furthers our understanding of how various types of cues interact in discourse processing and switches the focus from "what makes negation easier to process" to "what is made easier thanks to negation".