Extreme events occur in the complex system without generic early warning signals. When the predictability of the extreme events in complex systems is not possible, we can design an environment, which suppresses the extreme event from the systems. In this paper, we report the annihilation of extreme events in thedynamical system under environmental coupling. We consider two systems such as CO$_2$ laser and FitzHugh–Nagumo neuron models to examine the suppression of extreme events. When the systems are coupled with anenvironment, depending on the coupling strength the probability for the occurrence of extreme events decreases and after a critical coupling strength, the extreme events are annihilated from the system.