In this paper, we consider the problem of solving finite element equations of biharmonic Dirichlet problems. We divide the given domain into non-overlapping subdomains, construct a preconditioner for Morley element by substructuring on the basis of a function decomposition for discrete biharmonic functions. The function decomposition is introduced by partitioning these finite element functions into the low and high frequency components through the intergrid transfer operators between coarse mesh and fine mesh, and the conforming interpolation operators. The method leads to a preconditioned system with the condition number bounded by $C(1+\log^2H/h)$ in the case with interior cross points, and by $C$ in the case without interior cross points, where $H$ is the subdomain size and $h$ is the mesh size. These techniques are applicable to other nonconforming elements and are well suited to a parallel computation.