  We present two new one-parameter families of scheme transformations and apply
these to study the scheme dependence of the infrared zero in the beta function
of an asymptotically free non-Abelian gauge theory up to four-loop order. Our
results provide a further quantitative measure of this scheme dependence,
showing that for moderate values of the gauge coupling and the parameter
specifying the scheme transformation, this dependence is relatively mild. We
also remark on a generalized multi-parameter family of rational scheme
transformations.
