In this paper, we argue that the possibility of contesting the results of Algorithmic Decision Systems (ADS) is a key requirement for ADS used to make decisions with a high impact on individuals. We discuss the limitations of explanations and motivate the need for better facilities to contest or justify the results of an ADS. While the goal of an explanation is to make it possible for a human being to understand, the goal of a justification is to convince that the decision is good or appropriate. To claim that a result is good, it is necessary (1) to refer to an independent definition of what a good result is (the norm) and (2) to provide evidence that the norm applies to the case. Based on these definitions, we present a challenge and justification framework including three types of norms, a proof-of-concept implementation of this framework and its application to a credit decision system.