A method for the mixing augmentation of the transverse injection of fuel in a Scramjet combustor is suggested. Based on the fact that the main factor controlling the mixing characteristics in transverse injection is the effective back-pressure (the pressure around the injection hole) it is tried to make a flow expansion near the injection port in order to reduce effective back-pressure. A three dimensional Navier-Stokes code adopting the upwind method of Roe#s flux difference splitting scheme is used. The k-w SST turbulence model turbulence model is used to calculate the turbulent viscosity. It is shown that the reducing of the effective back-pressure make it possible to increase the penetration distance and to increase the mixing rate without excessive losses of stagnation pressure. Also, it is shown that the streamwise vorticity generated by baroclinic torque has great influences on the mixing process.