  A real anti-symmetric tensor field was introduced to realize a holographic
magnetic ordered phase in our previous works. However, a more careful analysis
shows there is a vector ghost in the model. In this paper we present a modified
Lagrangian density for the anti-symmetric tensor, which is ghost free and
causality is well-defined, and keeps all the significant results in the
original model qualitatively. We show this modified Lagrangian density could
come from the dimensional compactification of $p$-form field in
String/M-theory. For static curved space-time, we also prove that this modified
model is ghost free and dose not violate causality. This new model offers a
solid foundation for the application of antisymmetric tensor field in
holographic duality, especially for the spontaneous magnetization.
