  We study the formal conjugacy properties of germs of complex analytic
diffeomorphisms defined in the neighborhood of the origin of ${\mathbb C}^{n}$.
More precisely, we are interested on the nature of formal conjugations along
the fixed points set. We prove that there are formally conjugated local
diffeomorphisms $\phi, \eta$ such that every formal conjugation $\hat{\sigma}$
(i.e. $\eta \circ \hat{\sigma} = \hat{\sigma} \circ \phi$) does not extend to
the fixed points set $Fix (\phi)$ of $\phi$, meaning that it is not
transversally formal (or semi-convergent) along $Fix (\phi)$.
  We focus on unfoldings of 1-dimensional tangent to the identity
diffeomorphisms. We identify the geometrical configurations preventing formal
conjugations to extend to the fixed points set: roughly speaking, either the
unperturbed fiber is singular or generic fibers contain multiple fixed points.
