We devise a new high-frequency covariance matrix estimator based on price durations which is guaranteed to be positive-definite. Both non-parametric and parametric versions are proposed. A comprehensive Monte Carlo simulation shows that this class of estimators are less biased, more efficient, and generate lower RMSE as well as QLIKE errors. Empirically, we apply both estimators to a global minimum variance portfolio allocation problem and find they can generate comparably low portfolio variance, higher Sharpe ratios, but with considerably lower portfolio turnovers. This matrix estimator is also shown empirically to be more well-conditioned.