One of the method to have a fast acquisition of GNSS signals is the parallel code-phase search, which uses the fast Fourier transform (FFT) to perform the correlation. A problem with this method is the potential sign transition that can happen between two code periods due to data or secondary code and lead to a loss of sensitivity or to the non-detection of the signal. A known straightforward solution consists in using two code periods instead of one for the correlation. However, in addition to increasing the complexity, this solution is not efficient since half of the points calculated are discarded. This led us to look for a more efficient algorithm. The algorithm proposed in this article transforms the initial correlation into two smaller correlations. When the radix-2 FFT is used, the proposed algorithm is more efficient for half of the possible sampling frequencies. It is shown for example that the theoretical number of operations can be reduced by about 21 %, and that the memory resources for an FPGA implementation can be almost halved.