  In the present paper, superconvergence of second order, after an appropriate
postprocessing, is achieved for both the two and three dimensional first order
rectangular Morley elements of biharmonic equations. The analysis is dependent
on superconvergence of second order for the consistency error and a corrected
canonical interpolation operator, which help to establish supercloseness of
second order for the corrected canonical interpolation. Then the final
superconvergence follows a standard postprocessing. For first order
nonconforming finite element methods of both two and three dimensional fourth
order elliptic problems, it is the first time that full superconvergence of
second order is obtained without an extra boundary condition imposed on exact
solutions. It is also the first time that superconvergence is established for
nonconforming finite element methods of three dimensional fourth order elliptic
problems. Numerical results are presented to demonstrate the theoretical
results.
