In an influential article, Marfurt suggested that the best scheme for computational wave propagation would involve an averaging of the consistent and lumped finite element approximations. Many authors have considered how this might be accomplished for first order approximation, but the case of higher orders remained unsolved.  We describe recent work on the dispersive and dissipative properties of a novel scheme for computational wave propagation obtained by averaging the consistent (finite element) mass matrix and lumped (spectral element) mass matrix. The objective is to obtain a hybrid scheme whose dispersive accuracy is superior to both of the schemes. We present the optimal value of the averaging constant for all orders of finite elements and proved that for this value the scheme is two orders more accurate compared with finite and spectral element schemes, and, in addition, the absolute accuracy is of this scheme is better than that of finite and spectral element methods.   Joint work with Hafiz Wajid, COMSATS Institute of Technology, Pakistan.