For the blind estimation of short-code direct sequence spread spectrum (DSSS) signal pseudo-noise (PN) sequences, the eigenvalue decomposition (EVD) algorithm, the singular value decomposition (SVD) algorithm and the double-periodic projection approximation subspace tracking with deflation (DPASTd) algorithm are often used to estimate the PN sequence. However, when the asynchronous time delay is unknown, the largest eigenvalue and the second largest eigenvalue may be very close, resulting in the estimated largest eigenvector being any non-zero linear combination of the really required largest eigenvector and the really required second largest eigenvector. In other words, the estimated largest eigenvector exhibits unitary ambiguity. This degrades the performance of any algorithm estimating the PN sequence from the estimated largest eigenvector. To tackle this problem, this paper proposes a spreading sequence blind estimation algorithm based on the rotation matrix. First of all, the received signal is divided into two-information-period-length temporal vectors overlapped by one-information-period. The SVD or DPASTd algorithm can then be applied to obtain the largest eigenvector and the second largest eigenvector. The matrix composed of the largest eigenvector and the second largest eigenvector can be rotated by the rotation matrix to eliminate any unitary ambiguity. In this way, the best estimation of the PN sequence can be obtained. Simulation results show that the proposed algorithm not only solves the problem of estimating the PN sequence when the largest eigenvalue and the second largest eigenvalue are close, but also performs well at low signal-to-noise ratio (SNR) values.