Based on the ideas from [
] and [
] we present a new finite element method for the Kirchhoff plate bending model [
]. The method uses
basis functions for the deflection and the rotation, i.e. the same approach as used for the Reissner-Mindlin model. To account for the effective shear force at the free boundary a stabilization term is added. We prove optimal a-priori and a-posteriori error estimates. The corresponding results from benchmark problems are also reported.