  Motivated by the idea of $J$-frame for a Krein space $\textbf{\textit{K}}$,
introduced by Giribet \textit{et al.} (J. I. Giribet, A. Maestripieri, F.
Mart\'inez Per\'{i}a, P. G. Massey, \textit{On frames for Krein spaces}, J.
Math. Anal. Appl. (1), {\bf 393} (2012), 122--137.), we introduce the notion of
$\zeta-J$-tight frame for a Krein space $\textbf{\textit{K}}$. In this paper we
characterize $J$-orthonormal basis for $\textbf{\textit{K}}$ in terms of
$\zeta-J$-Parseval frame. We show that a Krein space is richly supplied with
$\zeta-J$-Parseval frames. We also provide a necessary and sufficient condition
when the linear sum of two $\zeta-J$-Parseval frames is again a
$\zeta-J$-Parseval frame. We then generalize the notion of $J$-frame potential
in Krein space from Hilbert space frame theory. Finally we provided a necessary
and sufficient condition for a $J$-frame potential of the corresponding
$\zeta-J$-tight frame to be minimum.
