Substituting this expression to (3) we have the equation for magnetization in the usual form: with and This is one of the interesting results. Namely, the renormalization is strong because of negative value of coupling constant γ$_{m}$ . Furthermore, the renormalization of T$_{f}$ does not appear if T$_{f}$ > T$_{M}$ . In the case of T$_{f}$ = T$_{M}$ the coupling would not change the critical temperatures and no renormalization would occur. The explicit stable solutions of equation (6) for ˜ M in the case e = 0 are: We apply the solution obtained above to the discussion of selected magnetic and dielectric properties of BiMnO$_{3}$. To visualize the influence of the magnetoelectric coupling on the magnetic properties of BiMnO$_{3}$, we fitted the temperature and applied magnetic field dependences of the magne- tization, based on the data of Kimura [16] and Chiba [19]. In Fig. 1 we display the fitted 5 III. APPLICATION TO BiMnO$_{3}$ A. Magnetic properties A ( T ) ˜ M + B ˜ M 3 − h = 0 , (6) A ≡ A ( T ) = T T$_{M}$ (1 − γ$_{m}$ ) + γ$_{m}$ T$_{f}$ T$_{M}$ − 1 , (7) B = 1 − γ 2 m l . (8) One sees that the effective magnetic transition temperature T$_{RM}$ is renormalized by the magnetoelectrical coupling. Explicitly, since the renormalized transition temperature is determined from the condition A ( T$_{RM}$ ) = 0, this yields: T$_{RM}$ = 1 − γ$_{m}$ T$_{f}$ T$_{M}$ 1 − γ$_{m}$ · T$_{M}$. (9) ˜ M =      − ( 2 $_{3}$) 1 $^{3}$A ( 9 B $^{2}$h + √ 3 √ 4 A $^{3}$B$^{3}$+27 B $^{4}$h2 ) 1 3 + ( 9 B $^{2}$h + √ 3 √ 4 A $^{3}$B$^{3}$+27 B $^{4}$h2 ) 1 3 2 1 3 3 2 3 B , for h > 0 ( 2 $_{3}$) 1 $^{3}$A ( √ 3 √ 4 A $^{3}$B$^{3}$+27 B $^{4}$h$^{2}$− 9 B $^{2}$h ) 1 3 − ( √ 3 √ 4 A $^{3}$B$^{3}$+27 B $^{4}$h$^{2}$− 9 B $^{2}$h ) 1 3 2 1 3 3 2 3 B , for h < 0      (10)