  The properties of antihydrogen ($\bar{\rm H}$) have, thus far, been probed at
magnetic fields of $\sim 1$ T. It may be fruitful to perform some of these
measurements at magnetic fields approaching 0 T. In this case, there could
occur zeros in the magnitude of the $B$-field. The number and properties of the
magnetic field zeros are investigated. For typical magnetic field geometries in
$\bar{\rm H}$ traps, the zeros will occur as two groups of 5 closely spaced
points instead of as a single point. Except in special cases, results from
calculations show that these 10 zeros can be treated as independent sources of
spin flip probability. Although the behavior of Majorana spin flip near higher
order zeros should not be important in the $\bar{\rm H}$ traps, the probability
for spin flip is calculated for the case of a quadratic zero. Finally, results
are presented for a simple model of how magnetic field zeros would affect the
trapped population of $\bar{\rm H}$.
