We will introduce a relative version of imprimitivity bimodule and a relative version of strong Morita equivalence for pairs of C ∗ C^* -algebras ( A , D ) (\mathcal {A}, \mathcal {D}) such that D \mathcal {D} is a C ∗ C^* -subalgebra of A \mathcal {A} satisfying certain conditions. We will then prove that two pairs ( A 1 , D 1 ) (\mathcal {A}_1, \mathcal {D}_1) and ( A 2 , D 2 ) (\mathcal {A}_2, \mathcal {D}_2) are relatively Morita equivalent if and only if their relative stabilizations are isomorphic. In particular, for two pairs ( O A , D A ) (\mathcal {O}_A, \mathcal {D}_A) and ( O B , D B ) (\mathcal {O}_B, \mathcal {D}_B) of Cuntz–Krieger algebras with their canonical masas, they are relatively Morita equivalent if and only if their underlying two-sided topological Markov shifts ( X ¯ A , σ ¯ A ) (\overline {X}_A,\bar {\sigma }_A) and ( X ¯ B , σ ¯ B ) (\overline {X}_B,\bar {\sigma }_B) are flow equivalent. We also introduce a relative version of the Picard group Pic ( A , D ) {\operatorname {Pic}}(\mathcal {A}, \mathcal {D}) for the pair ( A , D ) (\mathcal {A}, \mathcal {D}) of C ∗ C^* -algebras and study them for the Cuntz–Krieger pair ( O A , D A ) (\mathcal {O}_A, \mathcal {D}_A) .