In a direct spectrum (DS) system, the PN code can be estimated by analyzing the singular vectors of the received data matrix in order to blind despread in a non-cooperative context. But as there are information data reversions in the analyzed data matrix, some parts of the estimated PN code may be invertible to the original PN code, which may bring about problems in the following despreading process. In order to solve this problem, a method to well reconstruct the PN code is proposed. This method is based on power detection. The combination scheme which has the maximum power is the best combination scheme that is most suitable to the original PN code. Simulation results show that the method can reconstruct the PN code very well, even if the signal-to-noise ratio is low.