This paper develops a new double sampling (DS) monitoring scheme, namely, the side-sensitive DS X chart, to monitor the process mean. The operational procedure is presented first followed by the exact form of the probability of the in-control process under the normality assumption. Finally, the performance of the new scheme is investigated by minimizing the out-of-control average run-length and extra quadratic loss function. It was observed that the proposed chart presents a better overall performance than the existing DS X chart. An illustrative example is given to facilitate the design and implementation of the new chart.