  A conforming discontinuous Galerkin finite element method is introduced for
solving the biharmonic equation. This method, by its name, uses discontinuous
approximations and keeps simple formulation of the conforming finite element
method at the same time. The ultra simple formulation of the method will reduce
programming complexity in practice. Optimal order error estimates in a discrete
$H^2$ norm is established for the corresponding finite element solutions. Error
estimates in the $L^2$ norm are also derived with a sub-optimal order of
convergence for the lowest order element and an optimal order of convergence
for all high order of elements. Numerical results are presented to confirm the
theory of convergence.
