In a detailed study of the problem of induced numerical artifacts in the Real Space (RS) High Resolution Electron Microscopy (HREM) image simulation, a δ-ε criterion in the RS method for simulating HREM images has been derived. This condition imposes a practical limitation in choosing the sampling interval δ and the slice thickness ε for the RS method. It has been found that when the δ-ε condition is satisfied and a much more accurate formula is used for calculating the propagating factor p(r), the RS method gives results in satisfactory agreement with the conventional FFT multi-slice (FFTMS) method, but saving coputational time and avoiding the computing divergence that may arise in the RS method.