  Let $A$ be a finite dimensional algebra over an algebraically closed field
$k$. Let $T$ be a tilting $A$-module and $B={\rm End}_A\ T$ be the endomorphism
algebra of $T$. In this paper, we consider the correspondence between the
tilting $A$-modules and the tilting $B$-modules, and we prove that there is a
one-one correspondence between the basic $T$-tilting $A$-modules in $T^{\perp}$
and the basic tilting $B$-modules in $^{\perp}(D_BT)$. Moreover, we show that
there is a one-one correspondence between the $T$-contravariantly finite
$T$-resolving subcategories of $T^{\perp}$ and the basic $T$-tilting
$A$-modules contained in $T^{\perp}$. As an application, we show that there is
a one-one correspondence between the basic tilting $A$-modules in $T^{\perp}$
and the basic tilting $B$-modules in $^{\perp}(D_BT)$ if $A$ is a
$1$-Gorenstein algebra or a $m$-replicated algebra over a finite dimensional
hereditary algebra.
