Quadratic covariation is a popular descriptive measure for the volatility of a multivariate price process. It is consistently estimated by the sum of outer products of high-frequency returns. The proposed realized outlyingness weighted covariation (ROWCov) is a weighted sum of outer products of high-frequency returns and downweights returns that, because of jumps or other reasons, are outliers under the Brownian semimartingale model. The ROWCov is positive semidefinite and remains consistent for the integrated covariance in the presence of a finite-activity jump process. We illustrate the usefulness of the estimator on five-minute returns on the transaction prices of the Dow Jones Industrial Average constituents.