The next generation Global Navigation Satellite Systems (GNSS), such as Galileo and Global Positioning System (GPS) modernization, will use signals with equal code and bit periods, resulting in a potential bit sign transition in each primary code period of the received signal segments. A bit sign transition occurring within an integration period usually causes a splitting of the Cross Ambiguity Function (CAF) main peak into two smaller side lobes along the Doppler shift axis in the search space and it may lead to an incorrect Doppler shift estimate, which results in a serious performance degradation of the acquisition system. This paper proposes a novel two steps based bit sign transition cancellation method which can overcome the bit sign transition problem and remove or mitigate the CAF peak splitting impairments. The performance of the proposed technique has been comprehensively evaluated with Monte Carlo simulations in terms of detection and false alarm probabilities, which are presented by Receiver Operating Characteristic (ROC) and Signal-to-Noise-Ratio (SNR) curves. The test results show that the proposed acquisition technique can provide improved performance in comparison with the state-of-the-art acquisition approaches.