  Assume that $\D$ is a Krull-Schmidt, Hom-finite triangulated category with a
Serre functor and a cluster-tilting object $T$. We introduce the notion of
relative cluster tilting objects, and $T[1]$-cluster tilting objects in $\D$,
which are a generalization of cluster-tilting objects. When $\D$ is
$2$-Calabi-Yau, the relative cluster tilting objects are cluster-tilting. Let
$\la={\rm End}^{op}_{\D}(T)$ be the opposite algebra of the endomorphism
algebra of $T$. We show that there exists a bijection between $T[1]$-cluster
tilting objects in $\D$ and support $\tau$-tilting $\la$-modules, which
generalizes a result of Adachi-Iyama-Reiten \cite{AIR}. We develop a basic
theory on $T[1]$-cluster tilting objects. In particular, we introduce a partial
order on the set of $T[1]$-cluster tilting objects and mutation of
$T[1]$-cluster tilting objects, which can be regarded as a generalization of
`cluster-tilting mutation'. As an application, we give a partial answer to a
question posed in \cite{AIR}.
