One of the most significant errors in the pseudo-range measurement performance of GNSSes (Global Navigation Satellite Systems) is their multipath error for high-precision applications. Several schemes to mitigate this error have been studied. Most of them, however, have been focused on the GPS (Global Positioning System) L1 C/A (Coarse/Acquisition) signal that was designed in the 1970s and is still being used for civil navigation. Recently, several modernized signals that were especially conceived to more significantly mitigate multipath errors have been introduced, such as Time Multiplexed and Composite Binary Offset Carrier (TMBOC and CBOC, respectively) signals. Despite this advantage, however, a problem remains with the use of TMBOC and CBOC modulations: the ambiguity of BOC (Binary Offset Carrier)-modulated signal tracking. In this paper, a novel unambiguous multipath error mitigation scheme for these modernized signals is proposed. The proposed scheme has the same complexity as HRCs (High Resolution Correlators) but with low ambiguity. The simulation results showed that the proposed scheme outperformed or performed at par with the HRC in terms of their multipath error envelopes and running averages in the static and statistical channel models. The ranging error derived by the mean multipath error of the proposed scheme was below 1.8 meters in an urban area in the statistical channel model.