  A 4-dimensional Riemannian manifold equipped with an additional tensor
structure, whose fourth power is the identity, is considered. This structure
has a circulant matrix with respect to some basis, i.e. the structure is
circulant, and it acts as an isometry with respect to the metric.
  The Riemannian product manifold associated with the considered manifold is
studied.
  Conditions for the metric, which imply that the Riemannian product manifold
belongs to each of the basic classes of Staikova-Gribachev's classification,
are obtained.
  Examples of such manifolds are given.
