  We calculate isotope mass shift for several light ions using Dirac wave
functions and mass shift operator with relativistic corrections of the order of
$(\alpha Z)^2$. Calculated relativistic corrections to the specific mass shift
vary from a fraction of a percent for Carbon, to 2% for Magnesium. Relativistic
corrections to the normal mass shift are typically smaller. Interestingly, the
final relativistic mass shifts for the levels of one multiplet appear to be
even closer than for non-relativistic operator. That can be important for the
astrophysical search for possible $\alpha$-variation, where isotope shift is a
source of important systematic error. Our calculations show that for levels of
the same multiplet this systematics is negligible and they can be used as
probes for $\alpha$-variation.
