The evolution of the domain structure with the thickness of bcc Fe films deposited on the Ag(116) vicinal surface is studied by spin-polarized low-energy electron microscopy. We show that a spin reorientation transition proceeds via two mechanisms: continuous rotation of magnetization within the vertical plane perpendicular to the steps and discontinuous reorientation of the in-plane component of magnetization, leading to splitting of the domains. In contrast to previously investigated systems with stripe domains, we reveal that in the case of a vicinal ferromagnetic surface, the domain width increases while changing the orientation of the magnetization from a canted out-of-plane state into an in-plane state. A theoretical model developed in this work successfully describes the domain structure behavior observed in our experiments and can be equally applied to other ferromagnetic films grown on vicinal surfaces.