HHO methods [4, 1] rely on a pair of unknowns, attached to the mesh faces and the mesh cells. They offer various assets such as the support of polyhedral meshes, local conservation principles, optimal convergence rates, and computational efficiency.HHO methods are closely related to HDG and weak Galerkin methods [3]. [1, 2] successfully developed the HHO methods for wave propagation in (strongly) heterogeneous media. Explicit time-marching methods are preferred in the context of fast dynamics and nonlinear problems. However, when the wave equation is discretized using the second-order formulation in time, HHO methods lead to a semi-implicit problem. Indeed, the coupling between cells and faces unknowns requires the resolution of a static coupling each time step, either a coupled linear system inversion in the linear case, or a non-linear implicit problem in the non-linear case. In this last case, this is a costly operation. We present here an explicitation algorithm based on a splitting of the HHO operators. This splitting is iterated and converges to the expected solution, if the coefficient weighting the stabilization is large enough. We prove that the minimal value of the weighting coefficient is independent of the mesh-size. This splitting replaces the Newton algorithm by the iterative resolution of block diagonal linear system. Experiments on the preservation of optimal convergence rates and comparative computational costs will be reported.