  Let $\mathcal{C}_{k}^{-}$ be the set of all negative $C_k$. For odd cycle,
Wang, Hou and Li [29] gave a spectral condition for the existence of negative
$C_3$ in unbalanced signed graphs. For even cycle, we determine the maximum
index among all $\mathcal{C}_4^{-}$-free unbalanced signed graphs and
completely characterize the extremal signed graph in this paper. This could be
regarded as a signed graph version of the results by Nikiforov [23] and Zhai
and Wang [37].
