According to the non-identity problem, the descendants of victims of historical injustices do not have claims to compensation. Some authors have recently argued that while there are indeed no claims to compensation for the original injustices, such claims might be grounded in the continuing non-compensation for these injustices. In this article I analyze this ,,continuing injustice argument". Having introduced the argument, I defend it against three natural objections: the decoupling objection, the responsibility objection, and the information objection. It turns out that these objections weaken claims to compensation for continuing injustices to a lesser degree than it initially seems. But even if they did so strongly the continuing injustice argument could constitute a convincing answer to the non-identity problem. This is because the argument first and foremost only purports to show the possibility of (strong) claims to compensation, and not their actuality. It therefore does not entail a complete substantial theory of historical justice.