An efficient formulation for a 4-node shell element which includes the effect of large rotation increments is presented. The formulation is based on the MITC element proposed by Bathe et al. A complete and symmetric tangent stiffness matrix is obtained by considering up to the quadratic term of Taylor expansion of a finite rotation tensor. Several numerical examples are demonstrated to show the superior convergence by the present formulation compared with the conventional MITC formulation which assumes infinitesimal rotation increments. It is also shown in sensitivity analysis that accurate gradients are always obtained by the complete tangent stiffness, although erroneous gradients can be obtained by the conventional ones.