  We calculate the one-loop corrections to the mass and central charge of the
BPS monopole in N=2 super-Yang-Mills theory in 3+1 dimensions using a
supersymmetry-preserving version of dimensional regularization adapted to
solitons. In the renormalization scheme where previous studies have indicated
vanishing quantum corrections, we find nontrivial corrections that we identify
as the 3+1 dimensional analogue of the anomaly in the conformal central charge
of the N=1 supersymmetric kink in 1+1 dimensions. As in the latter case, the
associated contribution to the ordinary central charge has exactly the required
magnitude to preserve BPS saturation at the one-loop level. It also restores
consistency of calculations involving sums over zero-point energies with the
low-energy effective action of Seiberg and Witten.
