  The critical exponent corresponding to the renormalization of the composite
operator $\bar{\psi}\psi$ is computed in quantum electrodynamics at
$O(1/\Nf^2)$ in arbitrary dimensions and covariant gauge at the non-trivial
zero of the $\beta$-function in the large $\Nf$ expansion and the exponent
corresponding to the anomalous dimension of the electron mass which is a gauge
independent object is deduced. Expanding in powers of $\epsilon$ $=$ $2$ $-$
$d/2$ we check it is consistent with the known three loop perturbative
structure and determine the subsequent coefficients in the coupling constant
