  Let $G^{\sigma}=(G,\sigma)$ be a signed graph and $A(G,\sigma)$ be its
adjacency matrix. Denote by $m(G)$ the matching number of $G$. Let
$\eta(G,\sigma)$ be the nullity of $(G,\sigma)$. He et al. [Bounds for the
matching number and cyclomatic number of a signed graph in terms of rank,
Linear Algebra Appl. 572 (2019), 273--291] proved that
$$|V(G)|-2m(G)-c(G)\leq\eta(G,\sigma)\leq |V(G)|-2m(G)+2c(G),$$ where $c(G)$ is
the dimension of cycle space of $G$. Signed graphs reaching the lower bound or
the upper bound are respectively characterized by the same paper. In this
paper, we will prove that no signed graphs with nullity $|V(G)|-2m(G)+2c(G)-1$.
We also prove that there are infinite signed graphs with nullity
$|V(G)|-2m(G)+2c(G)-s,~(0\leq s\leq3c(G), s\neq1)$ for a given $c(G)$.
