  Let $G$ be a graph of order $n$. For every $v\in V(G)$, let $E_G(v)$ denote
the set of all edges incident with $v$. A signed $k$-submatching of $G$ is a
function $f:E(G)\longrightarrow \{-1,1\}$, satisfying $f(E_G(v))\leq 1$ for at
least $k$ vertices, where $f(S)=\sum_{e\in S}f(e)$, for each $ S\subseteq
E(G)$. The maximum of the value of $f(E(G))$, taken over all signed
$k$-submatching $f$ of $G$, is called the signed $k$-submatching number and is
denoted by $\beta ^k_S(G)$. In this paper, we prove that for every graph $G$ of
order $n$ and for any positive integer $k \leq n$, $\beta ^k_S (G) \geq n-k -
\omega(G)$, where $w(G)$ is the number of components of $G$. This settles a
conjecture proposed by Wang. Also, we present a formula for the computation of
$\beta_S^n(G)$.
