The sine-BOC (binary offset carrier) modulation is used in several signals of the new European Global Navigation Satellite System, Galileo, and modernized GPS. It provides these signals with enhanced robustness against multipath and increases the precision of the range measurement. However, this modulation presents some drawbacks. The most severe is the ambiguity problem in acquisition and tracking, which introduces a large bias in the pseudo-range measurement. In order to solve this problem, an unambiguous tracking technique for sine-BOC signals is proposed. This technique is based on a pseudo correlation function (PCF) which does not have any side peak and thus completely removes all of the false lock points on the discriminator output. Impacts of thermal noise and multipath on the proposed technique are investigated. Theoretical and numerical results obtained with BOC(n,n) and BOC(2n,n)$ signals show that this technique has a good noise mitigation performance and an average multipath performance.