  We consider the chiral expansion of the octet baryon magnetic moments in
heavy baryon chiral perturbation theory including all terms which are of order
$q^4$. These terms are formally of quadratic order in the quark masses. We show
that despite the large non-analytic quark mass corrections to the
Coleman-Glashow relations at order $q^3$, including all analytic and
non-analytic corrections at order $q^4$, which in total are of moderate size,
allows for a fit to the measured magnetic moments due to the appearance of
counter terms with free coupling constants of natural size. In this scheme, the
$\Lambda \Sigma^0$ transition moment is predicted to be $\mu_{\Lambda \Sigma^0}
= (1.42 \pm 0.01) \mu_N$.
