The microstructure of the magnetization reorientation in second-order perpendicular anisotropy approximation is theoretically studied by means of Monte Carlo simulations. The magnetic structure is investigated as a function of K₁^eff = K₁-E_D -the difference between first-order anisotropy and demagnetizing energy density-and the second-order anisotropy energy density K₂. For K₂>0 the transition from a vertical to in-plane orientation of the magnetization proceeds via the canting of magnetization. The canted phase consists of domains. The domain microstructure establishes the smooth, continuous connection between the vertical domain structure and the vortex structure for in-plane magnetization. For K₂<0 a continuous reorientation via a state of coexisting domains with vertical and in-plane magnetization is found. Within this state the size of the vertical and the in-plane domains depends on the ratio of K₁^eff and K₂ and changes continuously while the transition proceeds. Both, K₁^eff and K₂ determine the width and energy of the domain walls. The broadening and coalescing of domain walls found in first-order anisotropy approximation is prevented by the nonvanishing second-order contribution.