The critical exponent corresponding to the renormalization of the comp
osite operator psipsiBAR is computed in quantum electrodynamics at O(1
/N(f)2) in arbitrary dimensions and covariant gauge at the non-trivial
zero of the beta-function in the large N(f) expansion and the exponen
t corresponding to the anomalous dimension of the electron mass which
is a gauge independent object is deduced. Expanding in powers of epsil
on = 2 - d/2 we check it is consistent with the known three loop pertu
rbative structure and determine the subsequent coefficients in the cou
pling constant expansion to all orders in MSBAR.