A new method of element decomposition is introduced in the formulation of a new shell finite element. The actual element is decomposed into a translational element defined completely by the nodal translations and a difference element representing the difference between the actual element and the translational element. An alternative form of coordinate transformation is also suggested to achieve a simple and systematic formulation. Three different types of elements, designated as types I, II and III, are derived by employing different assumptions on the displacement field of each component element. The type III element, in which the rotation of the translational element and the translation of the difference element are suppressed, gives the most favorable results. The element has properties similar to Ahmad's degenerate shell element, but shows better performance than the latter for all test problems considered in this study.