  Let $R$ be a commutative unitary ring. An idempotent in $R$ is an element
$e\in R$ with $e^2=e$. The Erd\H{o}s-Burgess constant associated with the ring
$R$ is the smallest positive integer $\ell$ (if exists) such that for any given
$\ell$ elements (not necessarily distinct) of $R$, say $a_1,\ldots,a_{\ell}\in
R$, there must exist a nonempty subset $J\subset \{1,2,\ldots,\ell\}$ with
$\prod\limits_{j\in J} a_j$ being an idempotent. In this paper, we prove that
except for an infinite commutative ring with a very special form, the
Erd\H{o}s-Burgess constant of the ring $R$ exists if and only if $R$ is finite.
