  The aim of this paper is to establish the weak convergence, in the topology
of the Skorohod space, of the $\nu$-symmetric Riemann sums for functionals of
the fractional Brownian motion when the Hurst parameter takes the critical
value $H=(4\ell+2)^{-1}$, where $\ell=\ell(\nu)\geq 1$ is the largest natural
number satisfying $\int_0^1 \alpha^{2j}\nu(d\alpha)=(2j+1)^{-1}$ for all
$j=0,\ldots,\ell-1$. As a consequence, we derive a change-of-variable formula
in distribution, where the correction term is a stochastic integral with
respect to a Brownian motion that is independent of the fractional Brownian
motion.
