A numerical procedure was derived to perform direct simulations of compressible homogeneous sheared turbulence. In this type of direct simulations, the pseudo-spectral method has often been used with the grid-remeshing procedure. However, this approach causes critical interpolation errors of the aliasing type. In this study, therefore, the grid was fixed and the finite-difference scheme was used in the shear-normal direction. As a result, precise data for compressible homogeneous sheared turbulence were obtained which are useful in analyzing the effect of compressibility on turbulence.