We propose a new strategy for mean–variance portfolio selection that tackles transaction costs and change detection in covariance matrix simultaneously. The new strategy solely rebalances the portfolio when change points are detected in the covariance matrix, striking an optimal trade-off between rebalancing the portfolio to capturing the recent information in return data and avoiding excessive trading. Our empirical results suggest favorable out-of-sample performance of the new strategy in terms of portfolio variance, portfolio turnovers and portfolio sharpe ratio with transaction cost. We also show that these gains come from the improved accuracy for covariance matrix prediction and the ability for tracking significant changes in covariance matrix.