Evolution Strategies (ESs) usually rely on normally distributed additive variations of candidate solutions. Adaptation of the covariance matrix of the normal distribution allows efficient search in non-separable and ill-conditioned landscapes. To sample the distribution, the adapted covariance matrix needs to be decomposed. We propose a new update mechanism that can equivalently replace a rank-one covariance matrix update including the computationally expensive decomposition of the covariance matrix. The new update rule reduces the computational complexity from $O(n^3)$ to $O(n^2)$, where $n$ is the search space dimension.