Extracting surface wave travel time information from the cross-correlation (CC) of seismic ambient noise has been a great success and remains fast growing. However, it is still challenging to exploit the amplitude content of the noise CC. Although spatial average is able to constrain somewhat meaningful attenuation using noise CC amplitudes, clear bias is observed when spatially varying attenuation is estimated with the traditional noise CC calculation methods. Perhaps the key lies in the development of novel techniques that can mitigate the effect of the uneven distribution of natural noise sources. In this paper, we propose a new method to use the correlation of the coda of correlation of noise (C3) for amplitude measurement. We examine the ability of the method to retrieve surface wave attenuation using data from selected line array stations of the USArray. By comparing C3-derived attenuation coefficients with those estimated from earthquake data, we demonstrate that C3 effectively reduces bias and allows for more reliable attenuation estimates from noise. This is probably because of the fact that the coda of noise correlation contains more diffused noise energy, and thus, the C3 processing effectively makes the noise source distribution more homogeneous. When selecting auxiliary stations for C3 calculation, we find that stations closer to noise sources (near the coast) tend to yield better signal-to-noise ratios. We suggest to preprocess noise data using a transient removal and temporal flattening method, to mitigate the effect of temporal fluctuation of the noise source intensity, and to retain relative amplitudes. In this study, we focus our analysis on 18 s measurements.