We present a new high ordermethod in space and time for solving the wave equation, based on a newinterpretation of the "Modified Equation" technique. Indeed, contrary to most of the works, we consider the time discretization before the space discretization. After the time discretization, an additional biharmonic operator appears, which can not be discretized by classical finite elements. We propose a new Discontinuous Galerkinmethod for the discretization of this operator, and we provide numerical experiments proving that the new method is more accurate than the classicalModified Equation technique with a lower computational burden.