Algorithms by stochastic methods to partial differential equations of the fourth order involving biharmonic operators are stated. The author considered a construction of the solution of a partial differential equation using a certain probability space and stochastic process. There are two algorithms for the fourth-order partial differential equations by stochastic methods. The first one is the method using signed measures. This is a methodwhich constructs a signed measure by a solution using the Fourier transform and obtains a coordinate mapping process. The second method uses iterated Brownian motion. The latter is treated in this paper. The definition ofiterated Brownian motion was modified to investigate the properties of its distribution. The author also defined an iterated random walk corresponding to discretization of that, and showed that it converges to an iteratedBrownian motion in law to the iterated Brownian motion, and obtained its order. In the conventional method, the partial differential equation of the fourth order corresponding to iterated Brownian motion, the Laplacian ofthe boundary condition arises in the remainder term. In other words, if the boundary condition is harmonic, the representation of the partial differential equation involving the biharmonic operator is possible.By focusing on the distribution of the iterated Brownian motion, the representation of the partial differential equation including the biharmonic operator is possible when the boundary condition is biharmonic.