The scenario of the magnetization reorientation in second-order perpendicular anisotropy approximation is theoretically studied by means of Monte-Carlo simulations. The microstructure is investigated as a function of the difference between first-order anisotropy and demagnetizing energy Keff = K1-ED and the second-order anisotropy K2. An influence of the second-order perpendicular anisotropy on the spin reorientation transition is found when Keff vanishes. The broadening and coalescing of domain walls found earlier for K2 = 0 is prevented by positive K2. The domain wall width and energy are determined by K2. For K2>0 the transition via a canted vortex-like structure is found which yields the smooth, continuous connection between the vertical domain structure and the vortex structure with in-plane magnetization. (@@@)