The present paper focuses on the development of a novel ExGA-based time-marching scheme applied to the scalar wave equation. The formulation of the domain boundary element method (D-BEM), characterized by the use of static fundamental solutions, preserves the domain integral of inertial terms giving rise to an equation similar to that provided by the finite element method after space discretization is carried out. This equation can be solved in time using time-stepping algorithms, such as Newmark or Houbolt methods. However, in this work Green's functions are explicitly calculated and then incorporated into a time-marching procedure, whose results show good accuracy and stability. Two typical examples are presented to illustrate the accuracy and stability of this approach. (C) 2010 Elsevier Ltd. All rights reserved.