In this paper, we propose a new approach to prove stability of non-linear discrete-time systems. After introducing the new concept of stability contractor, we show that the interval centred form plays of fundamental role in this context and makes it possible to easily prove asymptotic stability of a discrete system. Then, we illustrate the principle of our approach through theoretical examples. Finally, we provide two practical examples using our method : proving stability of a localisation system and that of the trajectory of a robot.