This study explores effects of the nontraditional Coriolis terms (NCTs) on convective system propagation in radiative-convective equilibrium (RCE). NCTs are restored to the System for Atmospheric Modeling (SAM) to explicitly simulate the temporal evolution of convective systems in a zonal vertical domain rotating about a meridional axis. The system rotation rate is tested over a wide range. The results are transformed into space-time spectra to analyze the overall propagation characteristics. The raw spectra show local power maxima in bands associated with self-aggregated convection and convectively coupled gravity waves. Changes in the spectra due to the inclusion of NCTs can mostly be explained by the compressional beta effect (CBE), which speeds up the eastward propagation and slows down the westward propagation of zonal vertical circulation. For example, given the power spectra red in frequency, the power increases in the band of eastward propagating convective clusters and decreases in the band of westward ones. Furthermore, the speed changes of convectively coupled gravity waves are measured from the spectra. The magnitude of the speed changes increases with the system rotation rate, and this increase agrees with the theoretical speed change due to the CBE. These results suggest that the dry CBE theory can explain the effect of NCTs on the propagation of convective systems. This study recommends the restoration of NCTs to model dynamical cores because NCTs meaningfully correct the propagation speed of convectively coupled circulations and computationally costs little.  SIGNIFICANCE STATEMENT The rotation of Earth turns eastward motion upward and upward motion westward, and vice versa. This effect is called the nontraditional Coriolis effect and is omitted in most of the current atmospheric models for predicting weather and climate. Using an idealized model with cloud physics, this study suggests that the inclusion of the nontraditional Coriolis effect speeds up eastward moving rainy systems and slows down westward moving ones. The speed change agrees with a theory without cloud physics. This study encourages restoring the nontraditional Coriolis effect to the atmospheric models since it increases the accuracy of tropical large-scale weather prediction while the cost is low.