  It is commonly stated that because terms in the beta function of a theory at
the level of $\ell \ge 3$ loops and higher are scheme-dependent, it is possible
to define scheme transformations that can be used to remove these terms, at
least in the vicinity of zero coupling. We prove that this is not, in general,
possible in the situation where a beta function is not identically zero but has
a vanishing one-loop term.
