The purpose of received signal strength (RSS) correction in radio-map based Wi-Fi localization is to obtain a set of fine-grain location-dependent RSS fingerprints, and eventually achieve the purpose of highly accurate and reliable localization. To meet this goal, the RSS correction is conducted on the raw RSS samples to eliminate the environmental noise from the radio-map. This paper shows the comprehensive analysis on the autocorrelation property of the chronological RSS samples in the same RSS sequence, and meanwhile presents the correlated RSS correction approach. Furthermore, the correlated RSS correction approach can also be integrated into the conventional radio-map based K nearest neighbor (KNN) and weighted KNN (WKNN) localization algorithms. The experimental results conducted on the real Wi-Fi RSS samples recorded in a representative indoor environment prove that the proposed correlated RSS correction approach can result in the significant improvement of accuracy over the conventional radio-map based localization.