Assessment of dynamic functional brain connectivity (dFC) based on fMRI data is an increasingly popular strategy to investigate temporal dynamics of the brain’s large-scale network architecture. Current practice of assessing dynamic changes in functional fMRI connectivity over time uses the Fisher transform onto connectivity values aiming to make brain connectivity adhere to an approximate normal distribution, thus stabilizing the signal variance. The Fisher transform creates an approximate normal distribution based on every single time-point for every single connection that is tested (i.e. multiple time series). It becomes unclear how well the stabilization of signal variance offered by the Fisher transform performs in the case of each time series, which generally have non-zero means. This is of importance because subsequent analysis steps are performed on each time series entailing that these should follow an approximate normal distribution. In this paper, using simulations and analysis of resting-state fMRI data, the effect of different variance stabilization strategies on connectivity time series, namely the Fisher transform, the Box Cox transform and a combined approach. If the intention of stabilizing the variance is, as often is the case, to quantify the fluctuations of each brain connectivity time series by sampling fluctuations from a normal distribution, we show that the usage of the Fisher transform is not optimal and may even skew a time series away from normality. Further, we show the suboptimal performance of the Fisher transform can be substantially improved by including an additional Box-Cox transformation after the dFC time series has been Fisher transformed. We show that our suggested method brings further improvement to transform the individual dFC time series towards an approximate normal distribution.