  The renormalization that relates a coupling "a" associated with a distinct
renormalization group beta function in a given theory is considered.
Dimensional regularization and mass independent renormalization schemes are
used in this discussion. It is shown how the renormalization $a^*=a+x_2a^2$ is
related to a change in the mass scale $\mu$ that is induced by renormalization.
It is argued that the infrared fixed point is to be a determined in a
renormalization scheme in which the series expansion for a physical quantity
$R$ terminates.
