  Majorana bound states appearing in 1-D $p$-wave superconductor ($\cal{PWS}$)
are found to result in exotic quantum holonomy of both eigenvalues and the
eigenstates. Induced by a degeneracy hidden in complex Bloch vector space,
Majorana states are identified with a pair of exceptional point ($\cal{EP}$)
singularities. Characterized by a collapse of the vector space, these
singularities are defects in Hilbert space that lead to M$\ddot{\rm o}$bius
strip-like structure of the eigenspace and singular quantum metric. The
topological phase transition in the language of $\cal{EP}$ is marked by one of
the two exception point singularity degenerating to a degeneracy point with non
singular quantum metric. This may provide an elegant and useful framework to
characterize the topological aspect of Majorana fermions and the topological
phase transition.
