Galileo and Modernized GPS have included in their signal structures a new signal modulation: the Binary Offset Carrier (BOC). In the navigation field, this modulation is characterized by the chipping rate of its spreading code (m×1.023 MHz) and the frequency of its square sub-carrier (n×1.023 MHz). As a consequence, it is usually referred to as a BOC(n,m) modulation. The choice of the parameters n and m has a significant impact on the signal tracking performance and characteristics [1]. It is well known that each BOC modulation brings many improvements when compared against a classical Bi-Phase Shift Keying (BPSK) modulation with the same chipping rate [1]. Among other examples, it provides a lower code tracking error in thermal noise, better multipath mitigation, and better rejection of narrow-band interference. However, its multi-peak autocorrelation function is a major drawback. This implies that when using classical acquisition and tracking techniques, there is a possibility of detecting and tracking the signal by locking onto a side-peak. This can lead to severe undesirable measurement biases when not corrected. Several methods have been developed in order to prevent such an event to occur [2, 3, 4, and 5]. These methods are usually generic to all BOC modulations. However, they have to incorporate trade-offs, such as a degraded code tracking accuracy, or the risk of a certain period of potential false peak tracking. This research uses a different approach to the problem. Instead of trying to find a generic solution, it was decided to study this ambiguity problem on a particular signal in order to try to apply relevant methods using this specific signal?s characteristics. The BOC modulation chosen was the sine-BOC(n,n) (sine- stands for the use of a sine square as the sub-carrier). This decision was motivated by the fact a sine-BOC(1,1) will most likely be used for the Galileo civil signal on L1, and potentially on GPS III [6, 7]. Moreover, the Galileo L1 signal will constitute the main Galileo signal for mass market applications due to its narrow frequency bandwidth and low sampling frequency required for its processing. As a result, finding an optimal way to track Galileo BOC(1,1) unambiguously is critical, as well as very challenging. This paper presents a new unambiguous BOC tracking method that can be applied to any sine-BOC(n,n) signal. It consistently removes the bias threat while having a close-to-optimum tracking accuracy. Sine-BOC modulation will be referred to as BOC modulation for simplicity throughout this paper. The first part focuses on the shortcomings of traditional BOC(n,n) tracking and the second part offers a detailed description of the new proposed method. The third part then focuses on the theoretical tracking performance of the proposed method in thermal noise only. Its behaviour in a multipath environment is then investigated before some simulation results are shown in the last section.