Since scaling exponents fitted from many fast Fourier transformation (FFT) power spectra of the log-intensity of laser beam in the turbulent atmosphere go beyond the theoretical bound, the discrete wavelet transformation (DWT) power spectrum was introduced. The superiority of DWT over FFT is verified through comparison of the scaling exponents fitted from the FFT and DWT power spectra of 1/f noises. The scaling exponents in the scaling region of the DWT power spectrum of laser scintillation vary smoothly in a whole day (except sunrise and sunset time) and lie in the bound. It is suggested that DWT instead of FFT should be used in the spectrum analysis of laser scintillation.