We compute the one-loop non-holomorphic effective potential for the N=4 SU(
n) supersymmetric Yang-Mills theory with the gauge symmetry broken down to
the maximal torus U(1)(n-1). Our approach remains powerful for arbitrary ga
uge groups and is based on thr use of N = 2 harmonic superspace formulation
for general N = 2 Yang-Mills theories along with the superfield background
field method. (C) 1999 Elsevier Science B.V. All rights reserved.