In the conventional $s\text{\ensuremath{-}}d$ model of magnetization dynamics, it is assumed that for an adiabatic situation the $s$ magnetization is ferromagnetically aligned to the $d$ magnetization. For configurations with strong noncollinearity in the $d$ magnetization, this no longer holds true for all cases. In the present paper it is shown that, as a consequence of this noncollinearity between the adiabatic $s$ and $d$ magnetizations, there arise several additional torques in the micromagnetic equation of motion for the $d$ magnetization. The equation is solved for a N\'eel wall driven by an external field and/or a spin-polarized current, yielding a correction term to the result of the conventional theory. By calculations with the ab initio density-functional electron theory, the magnitude of the correction term is estimated. It is concluded that for $3d$ metals the effects of the additional torques are very small except possibly for atomic-scale noncollinearities or for the long-term trajectories of complicated magnetization configurations.