  In this paper, we firstly extend Theorem 5.1.1 in \cite {Helein} due to
H\'elein to a rescaled branched conformal immersed sequence(c.f. Theorem 1.5).
By virtue of this local convergence theorem, we study the blowup behavior of a
sequence of branched conformal immersions of closed Riemannian surface in
$\mathbb{R}^{n}$ with uniformly bounded areas and Willmore energies.
Furthermore, we prove that the integral identity of Gauss curvature is true.
