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)
.