  Let $G$ be a simple graph and $A(G)$ be the adjacency matrix of $G$. The
matrix $S(G) = J -I -2A(G)$ is called the Seidel matrix of $G$, where $I$ is an
identity matrix and $J$ is a square matrix all of whose entries are equal to 1.
Clearly, if $G$ is a graph of order $n$ with no isolated vertex, then the
Seidel matrix of $G$ is also the adjacency matrix of a signed complete graph
$K_n$ whose negative edges induce $G$. In this paper, we study the Seidel
eigenvalues of the complete multipartite graph $K_{n_1,\ldots,n_k}$ and
investigate its Seidel characteristic polynomial. We show that if there are at
least three parts of size $n_i$, for some $i=1,\ldots,k$, then
$K_{n_1,\ldots,n_k}$ is determined, up to switching, by its Seidel spectrum.
