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Let $\mathcal{C}$ be a triangulated category with shift functor $[1]$ and$\mathcal{R}$ a rigid subcategory of $\mathcal{C}$. We introduce the notions oftwo-term $\mathcal{R}[1]$-rigid subcategories, two-term (weak)$\mathcal{R}[1]$-cluster tilting subcategories and two-term maximal$\mathcal{R}[1]$-rigid subcategories, and discuss relationship between them.Our main result shows that there exists a bijection between the set of two-term$\mathcal{R}[1]$-rigid subcategories of $\mathcal{C}$ and the set of$\tau$-rigid subcategories of $\mod\mathcal{R}$, which induces a one-to-onecorrespondence between the set of two-term weak $\mathcal{R}[1]$-clustertilting subcategories of $\mathcal{C}$ and the set of support $\tau$-tiltingsubcategories of $\mod\mathcal{R}$. This generalizes the main results in\cite{YZZ} where $\mathcal{R}$ is a cluster tilting subcategory. When$\mathcal{R}$ is a silting subcategory, we prove that the two-term weak$\mathcal{R}[1]$-cluster tilting subcategories are precisely two-term siltingsubcategories in \cite{IJY}. Thus the bijection above induces the bijectiongiven by Iyama-J{\o}rgensen-Yang in \cite{IJY}

Two-term relative cluster tilting subcategories, $\tau-$tilting modules and silting subcategories