The largest Lyapunov exponent is an important parameter of detecting and characterizing chaos produced from a dynamical system. Based on simulative calculation, it has been found that the largest Lyapunov exponent of the small scale wavelet transform modulus of a discrete dynamical system is the same as the system's. At the same time, the calculated results show that calculating the largest Lyapunov exponent with the small scale wavelet transform modulus can efficiently eliminate the effect of strong large scale noiss because of the high pass filtering characteristic of small scale wavelet transform.