We calculate the isotope mass shift for several light atoms and ions using Dirac wave functions and the massshiftoperator with relativistic corrections of the order of (ΑZ)².Calculated relativistic corrections to thespecific mass shift vary from a fraction of a percent for carbon to 2% for magnesium. Relativistic correctionsto the normal mass shift are typically smaller. Interestingly, the final relativistic mass shifts for the levels of onemultiplet appear to be even closer to each other than for nonrelativistic operators applied to Dirac functions.That can be important for the astrophysical search for possible Α variation, where the isotope shift is a sourceof important systematic error. Our calculations show that for levels of the same multiplet this systematics isnegligible, and they can be used as probes for Α variation.