In the theory of Riemannian holonomy groups there are two exceptional cases, the holonomy group G_2 in 7-dimensional and the holonomy group Spin(7) in 8-dimensional manifolds. In the present work, we investigate the structure of Riemannian manifolds whose holonomy group is a subgroup of Spin(7) for a special case. Manifolds with Spin(7) holonomy are characterized by the existence of a 4-form, called the Bonan form (Cayley form or Fundamental form), which is self-dual in the Hodge sense, Spin(7) invariant and closed. We review two methods for the construction of the Bonan form, based on the...