  We investigate the conjectured bound on the Lyapunov exponent for a charged
particle with angular motion in the Kerr-Newman-AdS black hole. The Lyapunov
exponent is calculated based on the effective Lagrangian. We show that the
negative cosmological constant reduces the chaotic behavior of the particle,
namely, it decreases the Lyapunov exponent. Hence, the bound is more effective
in the AdS spacetime than in the flat spacetime. Nevertheless, we find that the
bound can be violated when the angular momenta of the black hole are turned on.
Moreover, we show that in an extremal black hole, the bound is more easily
violated compared to the nonextremal black hole.
