A solution method for two-phase flow problems is presented that is very well established in numerical aerodynamics. The set of two-phase flow equations is presumed to be hyperbolic. The method solves the flow equation in its characteristic form (compatibility conditions) on a rectangular mesh. It uses the characteristic directions only to determine how the numerical solution depends on the upstream and downstream fluid flow states, in contrast to the method of characteristics. This results in a particular choice of backward and forward differences to approximate the spatial derivatives and yields a stable numerical scheme. The method works on a simple discrete mesh and does not need a staggered mesh for stability, as is widely used for two-phase flow calculations. Thereby, numerical diffusion is reduced and less computer time is needed because the equations of state are only evaluated at half the discrete points. The method is compared to a staggered mesh second-order method by solving different steady-state and transient two-phase flow problems (homogeneous equilibrium model).