  We introduce a new linear relation in the isotope shifts of atomic
spectroscopy. While the famous King relation is the linear relation among the
different transitions, the new one is the linear relation among the different
isotope pairs. Since we obtain this relation by exchanging the roles of the
electronic and the nuclear factors in the original relation, we call it the
dual King relation. This relation shows us similar information to the original
King relation without including new fit parameters when we measure the isotope
shifts of many transitions. In the dual King relation, the fit coefficients
consist of the nuclear factors. Then, the fit results give us constraints to
the ratios of the isotope dependence independent of the electron wave
functions. This helps us to test the origin of unknown higher order isotope
shifts. We show that the dual King relation can also be employed to constrain
the weakly interacting light new boson at the same level as the original King
relation.
