Abstract
It is shown that the formula of the isometry generators of the spinor representation given by Carter and McLenaghan is universal in the sense that this holds for any representation, in either local frames or even natural ones. Starting with the observation that point-dependent spin matrices in natural frames can be defined for any tensor representation, the covariant form of the isometry generators is written down, showing that this is just the Carter and McLenaghan formula in natural frames.