  Let $X\in\mathbb{C}^{m\times m}$ and $Y\in\mathbb{C}^{n\times n}$ be
nonsingular matrices, and let $N\in\mathbb{C}^{m\times n}$. Explicit
expressions for the Moore-Penrose inverses of $M=XNY$ and a two-by-two block
matrix, under appropriate conditions, have been established by
Castro-Gonz\'{a}lez et al. [Linear Algebra Appl. 471 (2015) 353-368]. Based on
these results, we derive a novel expression for the Moore-Penrose inverse of
$A+UV^{\ast}$ under suitable conditions, where $A\in \mathbb{C}^{m\times n}$,
$U\in \mathbb{C}^{m\times r}$, and $V\in \mathbb{C}^{n\times r}$. In
particular, if both $A$ and $I+V^{\ast}A^{-1}U$ are nonsingular matrices, our
expression reduces to the celebrated Sherman-Morrison-Woodbury formula.
Moreover, we extend our results to the bounded linear operators case.
