SAR raw data are usually oversampled and spectrally weighted along the Fourier-domain processing chain, to avoid Gibbs effects around point targets. During the range and azimuth SAR focusing operations, the use of matched filters, whose frequency responses are smoothed by means of tapering functions, such as Hamming, Taylor, or Kaiser windows, introduces a significant degree of spatial correlation of the noise in the single-look complex 2D signal at the output of the SAR processor. In this work, we make use an unsupervised procedure for the spatial decorrelation of fully-developed speckle, originally developed for improving the despeckling performance in the case of single-look SAR images [Lapini et al., 2014]. Now, the goal is evaluating the impact of a preliminary spatial decorrelation of the noise on the accuracy of temporal change detection between two single-look images of the same scene taken at different times. In a likely simulated scenario, we optionally introduce a spatial correlation of the noise in the synthetic complex data by means of a 2D separable Hamming window in the Fourier domain. Then, we remove such a correlation by using the whitening procedure, take the modulus of the SLC images, apply change detection algorithms suitable for detected data, and compare the geometric and radiometric accuracy of the estimated change maps for the three following cases: uncorrelated noise, correlated noise, and decorrelated noise. Several change detection methods are considered: from the simple Log-Ratio operator preceded by despeckling, to more advanced parametric or nonparametric methods based on the Kullback-Leibler divergence [Inglada and Mercier, 2007] or on the mean-shift clustering of the bivariate scatterplot [Aiazzi et al., 2013]. Simulation results show a consistent improvement of performance, notably the geometric accuracy of changes, but also their local extent. The benefits of noise decorrelation are noticeable in experiments carried out on true COSMO-SkyMed images.