The linear electrohydrodynamic instability of a non-Newtonian dielectric liquid sheet issued in an inviscid gas medium of different velocity has been investigated using the Oldroyd eight-constant model. The dispersion relations between the growth rates and wave numbers of both symmetric and antisymmetric disturbances are derived. Using a new simple numerical technique, the effects of various parameters included in the analysis, namely the electric field parameter, gas to liquid velocity ratio, gas and liquid dielectric constants, time constant ratio, liquid elasticity, liquid viscosity, gas to liquid density ratio, surface tension, and liquid sheet velocity on the growth rates of symmetric and antisymmetric disturbances are studied in detail. It is found that the antisymmetric disturbances always prevail over symmetric disturbances, and the applied electric field, elasticity number, liquid velocity, gas Weber number, and gas to liquid density ratio have destabilizing effects, while the time constant ratio, surface tension, and liquid viscosity have stabilizing effects. It is also found that the gas to liquid velocity ratio and the dielectric constants have dual roles on the stability of the system (stabilizing as well as destabilizing) under certain conditions. The effects of various parameters on both the maximum growth rates and the dominant wave numbers for symmetric and antisymmetric disturbances have been discussed in detail.