We show that the magnetic moments of the octet baryons can be fitted t
o an accuracy of 1.5% by a phenomenological Lagrangian in which SU(3)
breaking corrections appear only linearly. This is in contrast to conv
entional chiral perturbation theory in which corrections non-analytic
in SU(3) breaking dominate and tend to spoil the agreement with the da
ta. Motivated by this observation, we propose a modified scheme for ch
iral perturbation theory that gives rise to a similar linear breaking
of SU(3) symmetry.