Abstract In meteorological dynamics, the shallow-atmosphere approximation is generally used in the momentum equation, together with the “traditional approximation.” In the traditional approximation, two cosine Coriolis terms [hereafter called nontraditional Coriolis terms (NCTs)] and some metric terms are omitted. However, some studies have suggested that the omission of the NCTs may not be appropriate for conditions near the equator. Therefore, this paper investigates the effect of the NCTs on large-scale motions forced by local positive-only heating mimicking cumulus convection. The authors use the linearized quasihydrostatic equation system on an equatorial β plane. Prescribed heating is assumed to move eastward with the slow phase speed of an intraseasonal period. Results of scale analysis and numerical calculations show that differences with and without the NCTs (hereafter, contributions) exhibit the following four features. (i) Whereas contributions to horizontal divergence and vertical velocity are small, the NCTs have large effects on horizontal velocity (vertical vorticity) and perturbations of pressure, potential temperature, and density. (ii) Contributions to horizontal velocity and pressure perturbation have equivalent barotropic structure. (iii) Contributions show east–west asymmetric patterns, with large contributions appearing at the western side of the forcing. (iv) Contributions to vertical vorticity and pressure perturbation are extremely large when the meridional gradient of heating is large. These features can be comprehensively explained by the tilting of the meridional component of the planetary vorticity, which is caused by the meridional gradient of heating.