  Let $\Gamma=(G,\sigma)$ be a signed graph, where $\sigma$ is the sign
function on the edges of $G$. The adjacency matrix of $\Gamma=(G, \sigma)$ is a
square matrix $A(\Gamma)=A(G, \sigma)=\left(a_{i j}^{\sigma}\right)$, where
$a_{i j}^{\sigma}=\sigma\left(v_{i} v_{j}\right) a_{i j}$. In this paper, we
determine the eigenvalues of the signed complete bipartite graphs. Let $(K_{p,
q},\sigma)$, $p\leq q$, be a signed complete bipartite graph with bipartition
$(U_p, V_q)$, where $U_p=\{u_1,u_2,\ldots,u_p\}$ and
$V_q=\{v_1,v_2,\ldots,v_q\}$. Let $(K_{p, q},\sigma)[U_r\cup V_s]$, $r\leq p$
and $s\leq q $, be an induced signed subgraph on minimum vertices $r+s$, which
contains all negative edges of the signed graph $(K_{p, q},\sigma)$. We show
that the multiplicity of eigenvalue $0$ in $(K_{p, q},\sigma)$ is at least $
p+q-2k-2$, where $k=min(r,s)$. We determine the spectrum of signed complete
bipartite graph whose negative edges induce disjoint complete bipartite
subgraphs and path. We obtain the spectrum of signed complete bipartite graph
whose negative edges (positive edges) induce an $r-$ regular subgraph $H$. We
find a relation between the eigenvalues of this signed complete bipartite graph
and the non-negative eigenvalues of $H$.
