We will show how to get Burkholder's function from (Ann. Probab. 12 (1984) 647-702) by using Monge-Ampère equation. This method is quite different from those in the series of Burkholder's papers (Ann. Probab. 12 (1984) 647-702, An extension of classical martingale inequality (1986) Marcel Dekker, Astérisque 157-158 (1988) 75-94, In Harmonic analysis and partial differential equations (1989) 1-23 Springer, In École d'Ete de Probabilités de Saint-Flour XIX (1991) 1-66 Springer, Ann. Probab. 22 (1994) 995-1025, Studia Math. 91 (1988) 79-83).