  An exceptional cycle in a triangulated category with Serre functor is a
generalization of a spherical object. Suppose that $A$ and $B$ are Gorenstein
algebras, given a perfect exceptional $n$-cycle $E_*$ in $K^b(A\mbox{-}{\rm
proj})$ and a perfect exceptional $m$-cycle $F_*$ in $K^b(B\mbox{-}{\rm
proj})$, we construct an $A$-$B$-bimodule $N$, and prove the product
$E_*\boxtimes F_*$ is an exceptional $(n+m-1)$-cycle in
$K^b(\Lambda\mbox{-}{\rm proj})$, where $\Lambda=\begin{pmatrix}A & N\\ 0 & B
\end{pmatrix}$. Using this construction, one gets many new exceptional cycles
which is unknown before for certain class of algebras.
