In this work a new iterative scheme for biharmonic type equations is presented. It is based on the reduction of fourth order equations to a sequence of second order problems. The new scheme is an original combination of a global gradient conjugate method, a local biconjugate gradient stabilized method, and a mimetic discretization of the second order equations involved in the problem. Its convergence is analytically proved. Numerical results provide for the first time an evaluation of mimetic schemes performance in the context of biharmonic problems.