  We explore, in the context of AdS/CFT correspondence, the causality
constraints on the Noncritical Einstein-Weyl (NEW) gravity model in five
dimensions. The scalar and shear channels are considered as small metric
perturbations around an AdS black brane background. Our results show that
causality analysis on the propagation of these two channels imposes a new bound
on the coupling of the Weyl-squared terms in the NEW gravity. This new bound
imposes more stringent restrictions than those of the tachyon-free condition,
improving predictive power of the theory.
