  We propose a generalization of the Hodge $dd_c$-lemma to the case of
hyperk\"ahler manifolds. As an application of this result we derive the global
construction of the fourth order transgression of the Chern character forms of
hyperholomorphic bundles over compact hyperk\"ahler manifolds. At the second
part of the paper we consider the fourth order transgression for the infinite
dimensional bundle arising from local families of hyperk\"ahler manifolds. We
propose a local construction of the fourth order transgression of the Chern
character form. We derive an explicit expression for arising hypertorsion
differential form. It's zero-degree part may be expressed in terms of the
Laplace operators defined on the fibers of the local family.
