The process of magnetization reversal was studied in Fe/Si multilayered films in the temperature range 5-300 K using the magneto-optical longitudinal Kerr effect. Magnetic field induced phase transitions have been found in these multilayers. At room temperature the field dependences of Kerr rotation demonstrated the features associated with the phase transition from one noncollinear structure to another. With the temperature decrease the field of the phase transition decreases and below 170 K, when the noncollinear structure becomes stable in zero magnetic field, this phase transition is not observed. The data of the phase transition from noncollinear to collinear parallel structure have been also obtained. The H-T phase diagram has been constructed as the result of the magneto-optical investigations. Numerical calculation of H-T phase diagram has been made using the theory, which takes into account the competition between bilinear exchange, biquadratic exchange and cubic magnetic anisotropy as well as the change of the relation between bilinear and biquadratic exchange with temperature variation. The calculation demonstrates good agreement with experimental data.