A one-parameter single-frequency family of dark electromagnetic pulses that can propagate practically without being disturbed is obtained by performing extensive numerical simulations. The dark electromagnetic pulse related close to the solutions of the coupled nonlinear Schrdinger equations in one-dimensional LHMs is stable when parameter is lower and unstable when parameter is higher. With the same simulation conditions, the split dark electromagnetic pulse will become stable again by adding a frequency perturbation to the pulse, simultaneously appears a phenomenon that the velocity of the dark electromagnetic pulse becomes slow (or fast). This result provides a method for controlling the dark electromagnetic pulse split and its velocity in the coupled Left-handed Materials.