In this article we are interested in the semi-group stability for finite difference schemes approximations of hyperbolic systems of equations in corner domains. We give generalizations of the results of [10] and [9] from the half space geometry to the quarter space geometry. The most interesting fact is that the proofs of [10] and [9] can be adaptated with minor changes to apply in the quarter space geometry. This is due to the fact that both methods in [10] and [9] are based on energy methods and the construction of auxiliary problems with strictly dissipative boundary conditions which are known to be suitable for the strong well-posed for initial boundary value problems in the quarter space.