  Let $\Lambda = \left[\begin{array}{cc} A & 0 \\ M & B \end{array}\right] $ be
an Artin algebra and $_BM_A$ a $B$-$A$-bimodule. We prove that there is a
triangle equivalence $D_{sg}(\Lambda) \cong D_{sg}(A)\coprod D_{sg}(B)$ between
the corresponding singularity categories if $_BM$ is semi-simple and $M_A$ is
projective. As a result, we obtain a new method for describing the singularity
categories of certain bounded quiver algebras.
