Local enhancement of the power flow in a group front of a transient sinusoidal Gaussian beam refracted at the boundary of right- and left-handed media is observed. In vacuum the beam reaches a sinusoidal steady state that is a form of continuous wave (CW) Gaussian beam after 6 wave periods. Behind the interface plane in a low loss double negative medium with normal dispersion the individual Fourier components of the beam diffract at different angles and have diversified phase speeds. This results in the group front build-up that propagates on with the beam and moves sideways with respect to the group velocity direction, where energy is transported. The enhancement is illustrated with 2-D simulations using finite difference time domain (FDTD) method.