A recent paper by Eklund et al. (2012) showed that up to 70% false positive results may occur when analyzing functional magnetic resonance imaging (fMRI) data using the statistical parametric mapping (SPM) software, which may mainly be caused by insufficient compensation for the temporal correlation between successive scans. Here, we show that a blockwise permutation method can be an effective alternative to the standard correction method for the correlated residuals in the general linear model, assuming an AR(1)-model as used in SPM for analyzing fMRI data. The blockwise permutation approach including a random shift developed by our group (Adolf et al., 2011) accounts for the temporal correlation structure of the data without having to provide a specific definition of the underlying autocorrelation model. 1465 publicly accessible resting-state data sets were re-analyzed, and the results were compared with those of Eklund et al. (2012). It was found that with the new permutation method the nominal familywise error rate for the detection of activated voxels could be maintained approximately under even the most critical conditions in which Eklund et al. found the largest deviations from the nominal error level. Thus, the method presented here can serve as a tool to ameliorate the quality and reliability of fMRI data analyses.