The attitude algorithm of strapdown inertial navigation system (SINS) is a key part of its navigation algorithm.Describing the change of carriers attitude with quaternion has found a wide application in practical engineering,of which,the accuracy of initial quaternion extraction has a direct influence on the calculation accuracy of navigation.To this problem,on the basis of traditional extraction algorithms,an initial quaternion extraction algorithm based on K-matrix was obtained,and a comparative analysis of quaternion extraction with orthogonal and non-orthogonal initial attitude matrix was made.The extraction and verification of initial attitude matrix example showed that the extraction algorithm based on K-matrix has a lower computational complexity,and it can effectively improve the accuracy of quaternion extraction for non-orthogonal attitude matrix.The method provides a reference for improving initial quaternion extraction algorithm of attitude calculation.