Initial alignment is one of the key technologies in strapdown inertial navigation system (SINS) to provide initial state information for vehicle attitude and navigation. For some situations, such as the attitude heading reference system, the position is not necessarily required or even available, then the self-alignment that does not rely on any external aid becomes very necessary. This study presents a new self-alignment method under swaying conditions, which can determine the latitude and attitude simultaneously by utilizing all observation vectors without solving the Wahba problem, and it is different from the existing methods. By constructing the dyadic tensor of each observation and reference vector itself, all equations related to observation and reference vectors are accumulated into one equation, where the latitude variable is extracted and solved according to the same eigenvalues of similar matrices on both sides of the equation, meanwhile the attitude is obtained by eigenvalue decomposition. Simulation and experiment tests verify the effectiveness of the proposed methods, and the alignment result is better than TRIAD in convergence speed and stability and comparable with OBA method in alignment accuracy with or without latitude. It is useful for guiding the design of initial alignment in autonomous vehicle applications.