Numerical research has been done for the transverse jet behind a rearward-facings step in turbulent supersonic flow without chemical reaction. Purpose of transverse jet is to enhance mixing of the fuel in the combustor. Two-dimensional unsteady flowfields generated by slot injection into supersonic flow are numerically simulated with the Navier-Stokes equations with two-equation k-$varepsilon$ turbulence model. Numerical method is used high-order upwind TVD scheme. Eight cases are computed for different slot momentum flux ratios and slot position at downstream of the step. The flow is very similar to the cavity flow, because the jet acts as an obstacle. The numerical results thus show the periodic phenomenon.