We discuss the relative K-theory for a C*-algebra A, together with a C*-subalgebra A′ ⊆ A. The relative group is denoted Ki(A′;A), i = 0, 1, and is due to Karoubi. We present a situation where two pairs A′ ⊆ A and B′ ⊆ B are related so that there is a natural isomorphism between their respective relative K-theories. We also discuss applications to the case where A and B are C*-algebras of a pair of locally compact, Hausdorff topological groupoids, with Haar systems.