An improvement to the k-${varepsilon}$ turbulence model is presented and is shown to lead to better agreement with data regarding supersonic base flows. The improvement was achieved by imposing a grid-independent realizability constraint in the Launder-Sharma k-${varepsilon}$ model. The effects of compressibility were also examined. The numerical results show that the modified Launder-Sharma model leads to some improvement in the prediction of the velocity and turbulent kinetic energy profiles. Compressibility corrections also lead to better agreement in both the turbulent kinetic energy and the Reynolds stress profiles with the experimental data.