This result states bernstein theorem in dimension two: given u C 2(R 2) satisfy the minimal surface equation div ( u 1 + | u| 2 ) = 0 on R 2. Then there exist a 1, a 2, b R such that u(x 1, x 2) = a 1 x 1 + a 2 x 2 + b for every (x 1,.... It is useful in the structure and regularity of minimal surfaces, where variational identities, curvature estimates, and compactness arguments control geometric objects.