In deep metric learning targeted at time series, the correlation between feature activations may be easily enlarged through highly nonlinear neural networks, leading to suboptimal embedding effectiveness. An effective solution to this problem is whitening. For example, in online signature verification, whitening can be derived for three individual Gaussian distributions, namely the distributions of local features at all temporal positions 1) for all signatures of all subjects, 2) for all signatures of each particular subject, and 3) for each particular signature of each particular subject. This study proposes a unified method called total whitening that integrates these individual Gaussians. Total whitening rectifies the layout of multiple individual Gaussians to resemble a standard normal distribution, improving the balance between intraclass invariance and interclass discriminative power. Experimental results demonstrate that total whitening achieves state-of-the-art accuracy when tested on online signature verification benchmarks.