Recently, it has been found that noise can induce chaos and destruct the zero Lyapunov exponent in the situation where a nonchaotic attractor coexists with a nonattracting chaotic saddle, as in a periodic window [Phys. Rev. Lett. 88 (2002) 124101]. Here we report that noise can also destruct the zero Lyapunov exponent in coupled chaotic systems where there is only one attractor. Moreover, the zero Lyapunov exponent in noise free will become positive when adding noise and be proportional to the average frequency of bursting induced by noise. A physical theory and numerical simulations are presented to explain how the average frequency of bursting depends on the coupling and noise strength.